Bounded operators

R.A. Adams:Sobolev Spaces, Academic, New York 1975.MATHGoogle Scholar

N.I. Akhiezer, I.M. Glazman:Theory of Linear Operators in Hilbert space, 3r dedition, Viša Škola, Kharkov 1978 (in Russian; English translation of the 1st edition: F. Ungar Co., New York 1961, 1963).Google Scholar

S. Albeverioet al., eds.:Feynman Path Integrals, Lecture Notes in Physics, vol. 106, Springer, Berlin 1979.Google Scholar

S. Albeverioet al., eds.:Ideas and Methods in Quantum and Statistical Physics. R. Høegh—Krohn Memorial Volume, Cambridge University Press, Cambridge 1992.Google Scholar

S. Albeverio, F. Gesztesy, R. Høegh—Krohn, H. Holden:Solvable Models in Quantum Mechanics, 2nd edition, with an appendix by P. Exner, AMS Chelsea Publishing, Providence, RI, 2005MATHGoogle Scholar

S. Albeverio, R. Høegh—Krohn:Mathematical Theory of Feynman Path Integrals, Lecture Notes in Mathematics, vol. 523, Springer, Berlin 1976.Google Scholar

P.S. Alexandrov:Introduction to Set Theory and General Topology, Nauka, Moscow 1977 (in Russian).Google Scholar

W.O. Amrein:Non—Relativistic Quantum Dynamics, Reidel, Dordrecht 1981.MATHGoogle Scholar

W.O. Amrein, J.M. Jauch, K.B. Sinha:Scattering Theory in Quantum Mechanics. Physical Principles and Mathematical Methods, Benjamin, Reading, MA 1977.MATHGoogle Scholar

M.A. Antonec, G.M. Žislin, I.A. Šereševskii:On the discrete spectrum of N—body Hamiltonians, an appendix to the Russian translation of the monograph[[JW]], Mir, Moscow 1976 (in Russian).Google Scholar

A.O. Barut, R. Raczka:Theory of Group Representations and Applications,2nd edition, World Scientific, Singapore 1986.MATHGoogle Scholar

H. Baumgärtel, M. Wollenberg:Mathematical Scattering Theory, Akademie Verlag, Berlin 1983.Google Scholar

F.A. Berezin:The Second Quantization Method, 2nd edition, Nauka, Moscow 1986 (in Russian; English transl. of the 1st edition: Academic, New York1966).MATHGoogle Scholar

F.A. Berezin, M.A. Ŝubin:Schrödinger Equation, Moscow State University Publ., Moscow 1983 (in Russian; English translation: Kluwer, Dordrecht 1996).MATHGoogle Scholar

L.C. Biedenharn, J.D. Louck:Angular Momentum in Quantum Theory. Theory and Applications, Addison—Wesley, Reading, MA 1981.Google Scholar

M. Š. Birman, M.Z. Solomyak:Spectral Theory of Self-Adjoint Operators in Hilbert Space, Leningrad State University Lenninguad. 1980 (in Russian; English translation: Kluwer, Dordrecht 1987).Google Scholar

J.D. Bjorken, S.D. Drell:Relativistic Quantum Theory, I. Relativistic Quantum Mechanics, II. Relativistic Quantum Fields, McGraw—Hill, New York 1965.Google Scholar

H. Boerner:Darstellungen von Gruppen, 2.Ausgabe, Springer, Berlin 1967 (English translation: North-Holland, Amsterdam 1970).MATHGoogle Scholar

N.N. Bogolyubov, A.A. Logunov, A.I. Oksak, I.T. Todorov:General Principles of Quantum Field Theory, Nauka, Moscow 1987 (in Russian; a revised edition ofFoundations of the Axiomatic Approach to Quantum Field Theoryby the first two and the last author, Nauka, Moscow 1969;English translation: W.A. Benjamin, Reading, MA1975, referred to as [[ BLT ]]).Google Scholar

N.N. Bogolyubov, D.V. Širkov:An Introduction to the Theory of Quantized Fields, 4th edition, Nauka, Moscow 1984 (in Russian; English translation of the 3rd edition: Wiley—Interscience, New York1980).Google Scholar

D. Bohm :Quantum Theory, Prentice-Hall, New York 1952.MATHGoogle Scholar

O. Bratelli, D.W. Robinson:Operator Algebras and Quantum Statistical Mechanics I, II, Springer, New York 1979, 1981.Google Scholar

P. Busch, P.J. Lahti, P. Mittelstaedt:The Quantum Theory of Measurement, 2nd revised edition, Springer LNP m2, Berlin 1996.MATHGoogle Scholar

K. Chadan, P. Sabatier:Inverse Problems in Quantum Scattering Theory, 2nd edition, Springer, New York 1989.MATHGoogle Scholar

Tai—Pei Cheng, Ling—Fong Li:Gauge Theory of Elementary Particle Physics,Clarendon Press, Oxford 1984.Google Scholar

P.R. Chernoff:Product Formulas, Nonlinear Semigroups and Addition of Unbounded Operators, Mem. Amer. Math. Soc., Providence, RI 1974.Google Scholar

H.L. Cycon, R.G. Froese, W. Kirsch, B. Simon:Schrödinger operators, with Application to Quantum Mechanics and Global Geometry, Springer, Berlin 1987; corrected and extended 2nd printing, Springer, Berlin 2007.MATHGoogle Scholar

E.B. Davies:Quantum Theory of Open Systems, Academic, London 1976.MATHGoogle Scholar

E.B. Davies:One—Parameter Semigroups, Academic, London 1980.MATHGoogle Scholar

A.S. Davydov:Quantum Mechanics, 2nd edition, Nauka, Moscow 1973 (in Russian; English translation of the 1st edition: Pergamon Press, Oxford 1965).Google Scholar

Yu.N. Demkov, V.N. Ostrovskii:The Zero—Range Potential Method in Atomic Physics, Leningrad University Press, Leningrad 1975 (in Russian).Google Scholar

M. Demuth, P. Exner, H. Neidhardt, V.A. Zagrebnov, eds.:Mathematical Results in Quantum Mechanics, Operator Theory: Advances and Applications, vol. 70; Birkhäuser, Basel 1994.Google Scholar

J. Derezinski, Ch. Gerard:Scattering theory of classical and quantum N—particle systems, Texts and Monographs in Physics, Springer, Berlin 1997.Google Scholar

P.A.M. Dirac:The Principles of Quantum Mechanics, 4th edition, Clarendon Press, Oxford 1969.Google Scholar

J. Dittrich, P. Exner, eds.:Rigorous Results in Quantum Dynamics, World Scientific, Singapore 1991.MATHGoogle Scholar

J. Dittrich, P. Exner, M. Tater, eds.:Mathematical Results in Quantum Mechanics, Operator Theory: Advances and Appl., vol. 108; Birkhäuser, Basel 1999.Google Scholar

J. Dixmier:Les algèbres des opérateurs dans l'espace hilbertien (algèbres de von Neumann), 2me edition, Gauthier—Villars, Paris 1969.Google Scholar

J. Dixmier:Les C*—algèbras and leur représentations, 2me edition, Gauthier-Vilars, Paris 1969.Google Scholar

N. Dunford, J.T. Schwartz:Linear Operators, I. General Theory, II. Spectral Theory, III. Spectral Operators, Interscience Publications, New York 1958, 1962, 1971.Google Scholar

A.R. Edmonds:Angular Momentum in Quantum Mechanics, Princeton University Press, Princeton, NJ 1957; a revised reprint Princeton 1996.MATHGoogle Scholar

S.J.L. van Eijndhoven, J. de Graaf:A Mathematical Introduction to Dirac Formalism, North—Holland, Amsterdam 1986.MATHGoogle Scholar

G.G. Emch :Algebraic Methods in Statistical Mechanics and Quantum Field Theory, Wiley—Interscience, New York 1972.MATHGoogle Scholar

P. Exner:Open Quantum Systems and Feynman Integrals, D. Reidel, Dordrecht 1985.MATHGoogle Scholar

P. Exner, J. Keating, P. Kuchment, T. Sunada, A. Teplyaev, eds.:Analysison Graphs and Applications, Proceedings of the Isaac Newton Institute programme“Analysis on Graphs and Applications”, AMS “Contemporary Mathematics” Series, 2008Google Scholar

P. Exner, J. Neidhardt, eds.:Order, Disorder and Chaos in Quantum Systems,Operator Theory: Advances and Applications, vol. 46; Birkhäuser, Basel 1990.Google Scholar

P. Exner, P. Seba, eds.:Applications of Self—Adjoint Extensions in Quantum Physics, Lecture Notes in Physics, vol. 324; Springer, Berlin 1989.Google Scholar

P. Exner, P. Seba, eds.:Schrödinger Operators, Standard and Non—standard, World Scientific, Singapore 1989.Google Scholar

W. Feller:An Introduction to Probability Theory and Its Applications I, II, 3rd and 2nd edition, resp., Wiley, New York 1968, 1971.Google Scholar

R.P. Feynman:Statistical Mechanics. A Set of Lectures, W.A. Benjamin, Reading, MA. 1972.Google Scholar

R.P. Feynman, A.R. Hibbs:Quantum Mechanics and Path Integrals, McGraw— Hill, New York 1965.MATHGoogle Scholar

L. Fonda, G.C. Ghirardi:Symmetry Principles in Quantum Physics, Marcel Dekker, New York 1970.Google Scholar

I.M. Gel'fand, G.M. Silov:Generalized Functions and Operations upon Them, vol.I, 2nd edition, Fizmatgiz, Moscow 1959(in Russian; English translation: Academic, New York 1969).Google Scholar

I.M. Glazman:Direct Methods of Qualitative Analysis of Singular Differential Operators, Fizmatgiz, Moscow 1963(in Russian).Google Scholar

J. Glimm, A. Jaffe:Quantum Physics: A Functional Integral Point of View, 2nd edition, Springer, New York 1987.Google Scholar

A. Grothendieck:Produits tensoriels topologiques et espaces nucléaires, Mem. Am. Math. Soc., vol. 16, Providence, RI 1955.Google Scholar

R. Haag:Local Quantum Physics. Fields, Particles, Algebras, 2nd revised and enlarged edition Springer, Berlin 1996.MATHGoogle Scholar

P. Halmos:Measure Theory, 2nd edition, Van Nostrand, New York 1973.Google Scholar

P. Halmos:A Hilbert Space Problem Book, Van Nostrand, Princeton, NJ 1967.MATHGoogle Scholar

M. Hamermesh:Group Theory and Its Applications to Physical Problems, Addison-Wesley, Reading, MA. 1964.Google Scholar

G.H. Hardy, E.M. Wright:An Introduction to the Theory of Numbers, 5th edition, Oxford University Press, oxford 1979.MATHGoogle Scholar

B. Helffer: Semi—Classical Analysis for the Schrödinger Operator and Applications, Lecture Notes in Mathematics, vol. 1366, Springer, Berlin 1988.Google Scholar

E. Hille, R.S. Phillips: Functional Analysis and Semigroups, Am. Math. Soc. Colloq. Publ., vol. 31, Providence, Rhode Island 1957; 3rd printing 1974.Google Scholar

A.S. Holevo: Probabilistic and Statistical Aspects of the Quantum Theory, Nauka, Moscow 1980 (in Russian; English translation: North-Holland, Amsterdam 1982).Google Scholar

L. Hörmander: The Analysis of Linear Partial Differential Operators III, Springer, Berlin 1985; corrected reprint 1994.MATHGoogle Scholar

S.S. Horužii: An Introduction to Algebraic Quantum Field Theory, Nauka, Moscow 1986 (in Russian; English translation: Kluwer, Dordrecht 1990).Google Scholar

L. van Hove: Surcertaines représentations unitaires d‘un group infini des transformations, Memoires Acad. Royale de Belgique XXVI/6, Bruxelles 1951.Google Scholar

K. Huang: Statistical Mechanics, Wiley, New York 1963.Google Scholar

K. Huang: Quarks, Leptons and Gauge Fields, World Scientific, Singapore 1982.Google Scholar

N.E. Hurt: Geometric Quantization in Action, D. Reidel, Dordrecht 1983.MATHGoogle Scholar

C. Itzykson, J.—B. Zuber: Quantum Field Theory, McGraw—Hill, New York 1980.Google Scholar

V. Jarn ík: Differential Calculus II, 3rd edition, Academia, Prague 1976 (in Czech).Google Scholar

V. Jarník: Integral Calculus II, 2nd edition, Academia, Prague 1976 (in Czech).MATHGoogle Scholar

J.M. Jauch: Foundations of Quantum Mechanics, Addison-Wesley, Reading, MA 1968.MATHGoogle Scholar

T.F. Jordan: Linear Operators for Quantum Mechanics, Wiley, New York 1969.MATHGoogle Scholar

K. J örgens, J. Weidmann: Spectral Properties of Hamiltonian Operators, Lecture Notes in Mathematics, vol. 313, Springer, Berlin 1973.Google Scholar

E. Kamke: Differentialgleichungen realer Funktionen, Akademische Verlagsges-selschaft, Leipzig 1956.Google Scholar

D. Kastler, ed.: C‡-algebras and Their Applications to Statistical Mechanics and Quantum Field Theory, North—Holland, Amsterdam 1976.MATHGoogle Scholar

T. Kato: Perturbation Theory for Linear Operators, Springer, 2nd edition, Berlin 1976; reprinted in 1995.MATHGoogle Scholar

J.L. Kelley: General Topology, Van Nostrand, Toronto 1957; reprinted by Springer, Graduate Texts in Mathematics, No. 27, New York 1975.Google Scholar

A.A. Kirillov: Elements of the Representation Theory, 2nd edition, Nauka, Moscow 1978 (in Russian; French translation: Mir, Moscow 1974).Google Scholar

A.A. Kirillov, A.D. Gvišiani: Theorems and Problems of Functional Analysis, Nauka, Moscow 1979 (in Russian; French translation: Mir, Moscow 1982).MATHGoogle Scholar

J.R. Klauder, B.-S. Skagerstam, eds.: Coherent States. Applications in Physics and Mathematical Physics, World Scientific, Singapore 1985.MATHGoogle Scholar

W. Klingenberg: A Course in Differential Geometry, Springer, New York 1978.MATHGoogle Scholar

A.N. Kolmogorov, S.V. Fomin: Elements of Function Theory and Functional Analysis, 4th edition, Nauka, Moscow 1976 (in Russian; English translation of the 2nd ed.: Graylock 1961; French translation of the 3rd edition: Mir, Moscow 1974).Google Scholar

H.-H. Kuo: Gaussian Measures in Banach Spaces, Lecture Notes in Mathematics, vol. 463, Springer, Berlin 1975.Google Scholar

A.G. Kuroš: Lectures on General Algebra, 2nd edition, Nauka, Moscow 1973 (in Russian).Google Scholar

L.D. Landau, E.M. Lifšic: Quantum Mechanics. Nonrelativistic Theory, 3rd ed., Nauka, Moscow 1974 (in Russian; English translation: Pergamon, New York 1974).Google Scholar

P.D. Lax, R.S. Phillips: Scattering Theory, Academic, New York 1967; 2nd edition, with appendices by C.S. Morawetz and G. Schmidt, 1989.Google Scholar

E.H. Lieb, M. Loss: Analysis, 2nd edition, Graduate Studies in Mathematics, vol. 14, AMS, Providence, RI, 2001Google Scholar

E.H. Lieb, B. Simon, A.S. Wightman, eds.: Studies in Mathematical Physics. Essays in Honor of V. Bargmann, Princeton University Press, Pinceton, NJ 1976.Google Scholar

E.M. Loebl, ed.: Group Theory and Its Applications I–III, Academic, New York 1967.Google Scholar

J.T. Londergan, J.P. Carini, D.P. Murdock: Binding and Scattering in Two-Dimensional Systems. Applications to Quantum Wires, Waveguides and Photonic Crystals, Springer LNP m60, Berlin 1999.MATHGoogle Scholar

G. Ludwig: Foundations of Quantum Mechanics I, II, Springer, Berlin 1983,1985.Google Scholar

G. Ludwig: An Axiomatic Basis for Quantum Mechanics, I. Derivation of Hilbert Space Structure, Springer, Berlin 1985.Google Scholar

S. Lundquist, A. Ranfagni, Y. Sa—yakanit, L.S. Schulman: Path Summation: Achievements and Goals, World Scientific, Singapore 1988.Google Scholar

G. Mackey: Mathematical Foundations of Quantum Mechanics, Benjamin, New York 1963; reprinted by Dover Publications INC., Mineola, NY, 2004.MATHGoogle Scholar

G. Mackey: Induced Representations of Groups and Quantum Mechanics, W.A. Benjamin, New York 1968.MATHGoogle Scholar

S. MacLane, G. Birkhoff: Algebra, 2nd edition, Macmillan, New York 1979.Google Scholar

A.I. Markuševič: A Short Course on the Theory of Entire Functions, 2nd edition, Fizmatgiz, Moscow 1961 (in Russian; English translation: Amer. Elsevier 1966).Google Scholar

V.P. Maslov: Perturbation Theory and Asymptotic Methods, Moscow State University Publ., Moscow 1965 (in Russian; French translation: Dunod, Paris 1972).Google Scholar

V.P. Maslov, M.V. Fedoryuk: Semiclassical Approximation to Quantum Mechanical Equations, Nauka, Moscow 1976 (in Russian).Google Scholar

K. Maurin: Hilbert Space Methods, PWN, Warsaw 1959 (in Polish; English translation: Polish Sci. Publ., Warsaw 1972).MATHGoogle Scholar

A. Messiah: M écanique quantique I, II, Dunod, Paris 1959 (English translation: North—Holland, Amsterdam 1961, 1963).Google Scholar

C. Müller: Spectral Harmonics, Lecture Notes In Mathematics, vol. 17, Springer,Berlin 1966.Google Scholar

M.A. Naimark: Normed Rings, 2nd edition, Nauka, Moscow 1968 (in Russian; English translation: Wolters—Noordhoff, Groningen 1972).Google Scholar

M.A. Naimark: Linear Differential Operators, 2nd edition, Nauka, Moscow 1969 (in Russian; English translation of the 1st edition: Harrap & Co., London 1967, 1968).Google Scholar

M.A. Naimark:Group Representation Theory, Nauka, Moscow 1976 (in Russian; French translation: Mir, Moscow 1979).Google Scholar

J. von Neumann : Mathematische Grundlagen der Quantenmechanik, Springer Verlag, Berlin 1932 (English translation: Princeton University Press, Princeton, NJ 1955, reprinted 1996).MATHGoogle Scholar

R.G. Newton: Scattering Theory of Waves and Particles, 2nd edition, Springer Verlag, New York 1982; reprinted by Dover Publications Inc., Mineola, NY 2002.MATHGoogle Scholar

Y. Ohnuki, S. Kamefuchi: Quantum Field Theory and Parastatistics, Springer, Heidelberg 1982.MATHGoogle Scholar

K.R. Parthasarathy: Introduction to Probability and Measure, New Delhi 1980.Google Scholar

D.B. Pearson: Quantum Scattering and Spectral Theory, Techniques of Physics, vol. 9, Academic, London 1988.Google Scholar

P. Perry; Scattering Theory by the Enss Method, Harwood, London 1983.MATHGoogle Scholar

C. Piron: Foundations of Quantum Physics, W.A. Benjamin, Reading, MA 1976.MATHGoogle Scholar

L.S.Pontryagin:ContinuousGroups,3rd edition,Nauka,Moscow1973(inRussian; English translation of the 2nd edition: Gordon and Breach, New York 1966).Google Scholar

V.S. Popov: Path Integrals in Quantum Theory and Statistical Physics, Atom-izdat, Moscow 1976 (in Russian; English translation: D. Reidel, Dordrecht 1983).Google Scholar

E. Prugovečki: Quantum Mechanics in Hilbert Space, 2nd edition, Academic, New York 1981.MATHGoogle Scholar

M. Reed, B. Simon: Methods of Modern Mathematical Physics, I. Functional Analysis, II. Fourier Analysis. Self—Adjointness, III. Scattering Theory, IV. Analysis of Operators, Academic, New York 1972–79.Google Scholar

D.R. Richtmyer: Principles of Advanced Mathematical Physics I, Springer, New York 1978.MATHGoogle Scholar

F. Riesz, B. Sz.—Nagy: Lecons d'analyse fonctionelle, 6me edition, Akademic Kiadó, Budapest 1972.Google Scholar

W. Rudin: Real and Complex Analysis, 3rd edition, McGraw—Hill, New York 1987.MATHGoogle Scholar

W. Rudin: Functional Analysis, 2nd edition, McGraw—Hill, New York 1991.MATHGoogle Scholar

B.V. Šabat: Introduction to Complex Analysis, Nauka, Moscow 1969 (in Russ.).Google Scholar

S. Sakai: C*—Algebras and W*—Algebras, Springer, Berlin 1971.Google Scholar

R.Schatten: A Theoryof CrossSpaces,Princeton UniversityPress, Princeton,1950.Google Scholar

M. Schechter: Operator Methods in Quantum Mechanics, North—Holland, New York 1981; reprinted by Dover Publications Inc., Mineola, NY 2002.MATHGoogle Scholar

K. Schmüdgen: Unbounded Operator Algebras and Representation Theory, Akademie—Verlag, Berlin 1990.Google Scholar

L.S. Schulman: Techniques and Applications of Path Integration, Wiley—Inter-science, New York 1981.MATHGoogle Scholar

L. Schwartz: Théorie des distributions I, II, Hermann, Paris 1957, 1959.Google Scholar

L. Schwartz: Analyse Mathématique I, II, Hermann, Paris 1967.Google Scholar

S.S. Schweber: An Introduction to Relativistic Quantum Field Theory, Row, Peterson & Co., Evanston, IL 1961.Google Scholar

I.E. Segal: Mathematical Problems of Relativistic Physics, with an appendix by G.W. Mackey, Lectures in Appl. Math., vol. 2, American Math. Society, Providence, RI 1963.Google Scholar

E. Seiler: Gauge Theories as a Problem of Constructive Quantum Field Theory and Statistical Mechanics, Lecture Notes in Physics, vol. 159, Springer, Berlin 1982.Google Scholar

B. Simon: Quantum Mechanics for Hamiltonians Defined as Quadratic Forms, Princeton University Press, Princeton, NJ 1971.MATHGoogle Scholar

B. Simon: The P(Φ)2 Euclidian (Quantum) Field Theory, Princeton University Press, Princeton, NJ 1974.Google Scholar

B. Simon: Trace Ideals and Their Applications, Cambridge University Press, Cambridge 1979.MATHGoogle Scholar

B. Simon: Functional Integration and Quantum Physics, Academic, New York 1979; 2nd edition, AMS Chelsea Publishing, Providence, RI 2005.MATHGoogle Scholar

Ya.G. Sinai: Theory of Phase Transitions. Rigorous Results, Nauka, Moscow 1980 (in Russian).Google Scholar

A.N. Širyaev: Probability, Nauka, Moscow 1980 (in Russian).Google Scholar

A.A. Slavnov, L.D. Faddeev: Introduction to the Quantum Theory of Gauge Fields, Nauka, Moscow 1978 .(in Russian).Google Scholar

H.-J. Stöckmann: Quantum chaos. An introduction, Cambridge University Press, Cambridge, 1999.MATHGoogle Scholar

P. Stollmann: Caught by Disorder: Bound States in Random Media, Birkhäuser, Basel 2001.MATHGoogle Scholar

M.H. Stone: Linear Transformations in Hilbert Space and Their Applications to Analysis, Amer. Math. Colloq. Publ., vol. 15, New York 1932.Google Scholar

R.F. Streater, ed.: Mathematics of Contemporary Physics, Academic, London 1972.Google Scholar

R.F. Streater, A. Wightman: PCT, Spin, Statistics and All That, W.A. Benjamin, New York 1964.Google Scholar

A.S. Švarc: Mathematical Foundations of the Quantum Theory, Atomizdat, Moscow 1975 (in Russian).Google Scholar

A.E. Taylor: Introduction to Functional Analysis, 6th edition, Wiley, New York 1967.Google Scholar

J.R. Taylor: Scattering Theory. The Quantum Theory of Nonrelativistic Collisions, Wiley, New York 1972.Google Scholar

G. Teschl: Jacobi operators and completely integrable nonlinear lattices, Math. Surveys and Monographs, vol. 72; AMS, Providence, RI 2000.Google Scholar

B. Thaller: The Dirac Equation, Springer, Berlin 1992.Google Scholar

W. Thirring: A Course in Mathematical Physics, 3. Quantum Mechanics of Atoms and Molecules, 4. Quantum Mechanics of Large Systems, Springer, New York 1981, 1983.Google Scholar

V.M. Tikhomirov: Banach Algebras, an appendix to the monograph [[ KF ]] pp. 513–528 (in Russian).Google Scholar

B.R. Vainberg: Asymptotic methods in the Equations of Mathematical Physics, Moscow State University Publishing, Moscow 1982 (in Russian).Google Scholar

V.S. Varadarajan: Geometry of Quantum Theory I, II, Van Nostrand Reinhold, New York 1968, 1970.Google Scholar

V. Votruba: Foundations of the Special Theory of Relativity, Academia, Prague 1969 (in Czech).Google Scholar

R. Weder, P. Exner, B. Grebert, eds.: Mathematical Results in Quantum Mechanics, Contemporary Mathematics, vol. 307, AMS, Providence, RI 2002.Google Scholar

J. Weidmann: .Linear Operators in Hilbert Space, Springer, Heidelberg 1980 (2nd edition in German: Lineare Operatoren in Hilberträumen, I. Grundlagen, II. Anwendungen, B.G. Teubner, Stuttgart 2000, 2003).Google Scholar

E.P. Wigner: Symmetries and Reflections, Indiana University Press, Blooming-ton, IN 1971.Google Scholar

D.R. Yafaev: Mathematical Scattering Theory: General Theory, Transl. Math. Monographs, vol. 105; AMS, Providence, RI, 1992Google Scholar

K. Yosida: Functional Analysis, 3rd edition,Springer, Berlin 1971.MATHGoogle Scholar

D.P. Želobenko: Compact Lie Groups and Their Representations, Nauka, Moscow 1970 (in Russian).Google Scholar

A. Abrams, J. Cantarella, J.G. Fu, M. Ghomi, R. Howard: Circles minimize most knot energies, Topology 42 (2003), 381–394.MATHMathSciNetCrossRefGoogle Scholar

S.L. Adler: Quaternionic quantum field theory, Commun. Math. Phys. 104 (1986), 611–656.MATHADSCrossRefGoogle Scholar

D. Aerts, I. Daubechies: Physical justification for using the tensor product to describe two quantum systems as one joint system, Helv. Phys. Acta 51 (1978),661–675.MathSciNetGoogle Scholar

D. Aerts, I. Daubechies: A mathematical condition for a sublattice of a propo-sitional system to represent a physical subsystem, with a physical interpretation,Lett. Math. Phys. 3 (1979), 19–27.MATHADSMathSciNetCrossRefGoogle Scholar

J. Agler, J. Froese: Existence of Stark ladder resonances, Commun. Math.Phys. 100 (1985), 161–172.MATHADSMathSciNetCrossRefGoogle Scholar

S. Agmon, I. Herbst, E. Skibsted: Perturbation of embedded eigenvalues in the generalized N —body problem, Commun. Math. Phys. 122 (1989), 411–438.MATHADSMathSciNetCrossRefGoogle Scholar

J. Aguilar, J.—M. Combes: A class of analytic perturbations for one—body Schrödinger Hamiltonians, Commun. Math. Phys. 22 (1971), 269–279.MATHADSMathSciNetCrossRefGoogle Scholar

E. Akkermans, A. Auerbach, J. Avron, B. Shapiro: Relation between persistent currents and the scattering matrix, Phys. Rev. Lett. 66 (1991), 76–79.ADSCrossRefGoogle Scholar

S. Alama, P. Deift, R. Hempel: Eigenvalue branches of Schrodinger operator H — λW in a gap of σ(H), Commun. Math. Phys. 121 (1989), 291–321.MATHADSMathSciNetCrossRefGoogle Scholar

S. Albeverio: On bound states in the continuum of N—body systems and the virial theorem, Ann. Phys. 71 (1972), 167–276.ADSCrossRefGoogle Scholar

S. Albeverio, C. Cacciapuoti, D. Finco: Coupling in the singular limit of thin quantum waveguides, J. Math. Phys. 48 (2007), 032103.ADSMathSciNetCrossRefGoogle Scholar

S. Albeverio, R. Høegh—Krohn: Oscillatory integrals and the method of stationary phase, Inventiones Math. 40 (1977), 59–106.MATHADSCrossRefGoogle Scholar

S. Albeverio, L. Nizhnik: Approximation of general zero-range potentials,Ukrainian Math. J. 52 (2000), 582–589.MATHMathSciNetCrossRefGoogle Scholar

W.O. Amrein, M.B. Cibils: Global and Eisenbud—Wigner time delay in scattering theory, Helv. Phys. Acta 60 (1987), 481–500.MathSciNetGoogle Scholar

W.O. Amrein, V. Georgescu: Bound states and scattering states in quantum mechanics, Helv. Phys. Acta 46 (1973), 635–658.MathSciNetGoogle Scholar

J. Anderson: Extensions, restrictions and representations of C*—algebras,Trans. Am. Math. Soc. 249 (1979), 303–329.MATHCrossRefGoogle Scholar

J.—P. Antoine, F. Gesztesy, J. Shabani: Exactly solvable models of sphere interactions in quantum mechanics, J. Phys. A20 (1987), 3687–3712.ADSMathSciNetGoogle Scholar

J.—P. Antoine, A. Inoue, C. Trapani: Partial *—algebras of closed operators,I. Basic theory and the Abelian case, Publ. RIMS 26 (1990), 359–395.MATHMathSciNetGoogle Scholar

J.—P. Antoine, W. Karwowski: Partial *—algebras of Hilbert space operators,in Proceedings of the 2nd Conference on Operator Algebras, Ideals and Their Applications in Theoretical Physics (H. Baumgärtel et al., eds.), Teubner, Leipzig 1984;pp. 29–39.Google Scholar

A. Arai, H. Kawano: Enhanced binding in a general class of quantum field models, Rev. Math. Phys. 15 (2003), 387–423.MATHMathSciNetCrossRefGoogle Scholar

H. Araki: Type of von Neumann algebra associated with free field, Progr.Theor. Phys. 32 (1964), 956–965.MATHADSMathSciNetCrossRefGoogle Scholar

H. Araki: C*—approach in quantum field theory, Physica Scripta 24 (1981),981–985.MathSciNetCrossRefGoogle Scholar

H. Araki, J.—P. Jurzak: On a certain class of *—algebras of unbounded operators,Publ. RIMS 18 (1982), 1013–1044.MATHMathSciNetGoogle Scholar

H. Araki, Y. Munakata, M. Kawaguchi, T. Goto: Quantum Field Theory of Unstable Particles, Progr. Theor. Phys. 17 (1957), 419–442.MATHADSMathSciNetCrossRefGoogle Scholar

D. Arnal, J.—P. Jurzak: Topological aspects of algebras of unbounded operators,.J. Funct. Anal. 24 (1977), 397–425.MATHMathSciNetCrossRefGoogle Scholar

J. Asch, P. Duclos, P. Exner: Stability of driven systems with growing gaps.Quantum rings and Wannier ladders, J. Stat. Phys. 92 (1998), 1053–1069.MATHMathSciNetCrossRefGoogle Scholar

M.S. Ashbaugh, R.D. Benguria: Optimal bounds of ratios of eigenvalues of one—dimensional Schrödinger operators with Dirichlet boundary conditions and positive potentials, Commun. Math. Phys. 124 (1989), 403–415.MATHADSMathSciNetCrossRefGoogle Scholar

M.S. Ashbaugh, R.D. Benguria: A sharp bound for the ratio of the first two eigenvalues of Dirichlet Laplacians and extensions, Ann. Math. 135 (1992), 601–628.MathSciNetCrossRefGoogle Scholar

M.S. Ashbaugh, P. Exner: Lower bounds to bound state energies in bent tubes,Phys. Lett. A150 (1990), 183–186.ADSMathSciNetGoogle Scholar

M.S. Ashbaugh, E.M. Harrell II : Perturbation theory for resonances and large barrier potentials, Commun. Math. Phys. 83 (1982), 151–170.MATHADSMathSciNetCrossRefGoogle Scholar

M.S. Ashbaugh, E.M. Harrell II, R. Svirsky: On the minimal and maximal eigenvalue gaps and their causes, Pacific J. Math. 147 (1991), 1–24.MATHMathSciNetGoogle Scholar

M.S. Ashbaugh, C. Sundberg: An improved stability result for resonances,Trans. Am. Math. Soc. 281 (1984), 347–360.MATHMathSciNetCrossRefGoogle Scholar

A. Avila, S. Jitomirskaya: Solving the ten Martini problem, Lecture Notes in Physics 690(2006), 5–16.MathSciNetCrossRefADSGoogle Scholar

Y. Avishai, D. Bessis, B.M. Giraud, G. Mantica: Quantum bound states in open geometries, Phys. Rev. B44 (1991), 8028–8034.ADSGoogle Scholar

J. Avron: The lifetime of Wannier ladder states, Ann. Phys. 143 (1982), 33–53.ADSCrossRefGoogle Scholar

J. Avron, P. Exner, Y. Last: Periodic Schrödinger operators with large gaps and Wannier—Stark ladders, Phys. Rev. Lett. 72 (1994), 896–899.MATHADSCrossRefGoogle Scholar

J. Avron, A. Raveh, B. Zur: Adiabatic quantum transport in multiply connected systems, Rev. Mod. Phys. 60 (1988), 873–915.ADSMathSciNetCrossRefGoogle Scholar

J. Avron, R. Seiler, L.G. Yaffe: Adiabatic theorem and application to the quantum Hall effect, Commun. Math. Phys. 110 (1987), 33–49.MATHADSMathSciNetCrossRefGoogle Scholar

D. Babbitt, E. Balslev: Local distortion techniques and unitarity of the S—matrix for the 2—body problem, J. Math. Anal. Appl. 54 (1976), 316–349.MathSciNetCrossRefGoogle Scholar

V. Bach, J. Fröhlich, I.M. Sigal: Spectral analysis for systems of atoms and molecules coupled to the quantized radiation field, Commun. Math. Phys. 207(1999), 249–290.MATHADSCrossRefGoogle Scholar

V. Bargmann: On a Hilbert space of analytical functions and an associate integral transform I, II, Commun. Pure Appl. Math. 14 (1961), 187–214; 20 (1967),1–101.MATHMathSciNetCrossRefGoogle Scholar

V. Bargmann: Remarks on Hilbert space of analytical functions, Proc. Natl.Acad. Sci. USA 48 (1962), 199–204, 2204.MATHADSMathSciNetCrossRefGoogle Scholar

V. Bargmann: On unitary ray representations of continuous groups, Ann. Math.59 (1954), 1–46.MathSciNetCrossRefGoogle Scholar

V. Bargmann: Note on some integral inequalities, Helv. Phys. Acta 45 (1972),249–257.Google Scholar

V. Bargmann: On the number of bound states in a central field of forces, Proc.Natl. Acad. Sci. USA 38 (1952), 961–966.MATHADSMathSciNetCrossRefGoogle Scholar

F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, D. Sternheimer: Deformation theory and quantization I, II, Ann. Phys. 111 (1978), 61–110, 111–151.MATHADSMathSciNetCrossRefGoogle Scholar

H. Baumgärtel: Partial resolvent and spectral concentration, Math. Nachr. 69(1975), 107–121.MATHMathSciNetCrossRefGoogle Scholar

H. Baumgärtel, M. Demuth: Perturbation of unstable eigenvalues of finite multiplicity, J. Funct. Anal. 22 (1976), 187–203.MATHCrossRefGoogle Scholar

H. Baumgärtel, M. Demuth, M. Wollenberg: On the equality of resonances(poles of the scattering amplitude) and virtual poles, M. Nachr. 86 (1978), 167–174.MATHCrossRefGoogle Scholar

H. Behncke: The Dirac equation with an anomalous magnetic moment, Math.Z. 174 (1980), 213–225.MATHMathSciNetCrossRefGoogle Scholar

F.A. Berezin, L.D. Faddeev: A remark on Schrödinger's equation with a singular potential, Sov. Acad. Sci. Doklady 137 (1961), 1011–1014 (in Russian).MathSciNetGoogle Scholar

M. van den Berg: On the spectral counting function for the Dirichlet Laplacian,J. Funct. Anal. 107 (1992), 352–361.MATHMathSciNetCrossRefGoogle Scholar

M.V. Berry: Quantal phase factor accompanying adiabatic changes, Proc. Roy.Soc. London A392 (1984), 45–57.ADSMathSciNetGoogle Scholar

M.V. Berry: The adiabatic limit and the semiclassical limit, J. Phys. A17(1984), 1225–1233.ADSMathSciNetGoogle Scholar

M.V. Berry, K.E. Mount: Semiclassical approximations in wave mechanics,Rep. Progr. Phys. 35 (1972), 315–389.ADSCrossRefGoogle Scholar

A. Beskow, J. Nilsson: The concept of wave function and the irreducible representations of the Poincaré group, II. Unstable systems and the exponential decay law, Arkiv f¨ör Physik 34 (1967), 561–569.Google Scholar

G. Birkhoff, J. von Neumann: The logic of quantum mechanics, Ann. Math.37 (1936), 823–843.CrossRefGoogle Scholar

M.Š. Birman: On the spectrum of singular boundary problems, Mat. Sbornik 55 (1961), 125–174 (in Russian).MathSciNetGoogle Scholar

M.Š. Birman: Existence conditions for the wave operators, Doklady Acad. Sci.USSR 143 (1962), 506–509 (in Russian).MathSciNetGoogle Scholar

M.Š. Birman: An existence criterion for the wave operators. Izvestiya Acad.Sci. USSR, ser. mat. 27 (1963), 883–906 (in Russian).MATHMathSciNetGoogle Scholar

M.Š. Birman: A local existence criterion for the wave operators, Izvestiya Acad.Sci. USSR, ser. mat. 32 (1968), 914–942 (in Russian).MATHMathSciNetGoogle Scholar

J. Blank, P. Exner: Remarks on tensor products and their applications in quantum theory, I. General considerations, II. Spectral properties, Acta Univ. Carolinae, Math. Phys. 17 (1976), 75–89; 18 (1977), 3–35.MATHMathSciNetGoogle Scholar

J. Blank, P. Exner, M. Havlíček: Quantum—mechanical pseudo—Hamiltonians, Czech. J. Phys. B29 (1979), 1325–1341.ADSCrossRefGoogle Scholar

R. Blankenbecler, M.L. Goldberger, B. Simon: The bound states of weakly coupled long—range one—dimensional Hamiltonians, Ann. Phys. 108 (1977), 69–78.ADSMathSciNetCrossRefGoogle Scholar

D. Bollé, K. Chadan, G. Karner: On a sufficient condition for the existence of N—particle bound states, J. Phys. A19 (1986), 2337–2343.ADSGoogle Scholar

H.J. Borchers: Algebras of unbounded operators in quantum field theory, Physica 124A (1984), 127–144.ADSMathSciNetGoogle Scholar

D. Borisov, P. Exner: Exponential splitting of bound states in a waveguide with a pair of distant windows, J. Phys. A37 (2004), 3411–3428.ADSMathSciNetGoogle Scholar

D. Borisov, P. Exner, R. Gadyl'shin: Geometric coupling thresholds in a two—dimensional strip, J. Math. Phys. 43 (2002), 6265–6278.MATHADSMathSciNetCrossRefGoogle Scholar

D. Borisov, P. Exner, R. Gadyl'shin, D. Krejčiřík: Bound states in weakly deformed strips and layers, Ann. H. Poincaré 2 (2001), 553–572.MATHCrossRefGoogle Scholar

F. Boudjeedaa, L. Chetouani, L. Guechi, T.F. Hamman: Path integral treatment for a screened potential, J. Math. Phys. 32 (1991), 441–446.ADSMathSciNetCrossRefGoogle Scholar

J. Brasche, P. Exner, Yu. Kuperin, P. Šeba: Schrödinger operators with singular interactions, J. Math. Anal. Appl. 184 (1994), 112–139.MATHMathSciNetCrossRefGoogle Scholar

J. Brasche, A. Teta: Spectral analysis and scattering theory for Schrödinger operators with an interaction supported by regular curve, in the proceedings volume [[ AFHL ]], pp. 197–211.Google Scholar

J. Brüning, P. Exner, V. Geyler: Large gaps in point—coupled periodic systems of manifolds, J. Phys. A: Math. Gen. 36 (2003), 4875–4890.MATHADSCrossRefGoogle Scholar

J. Brüning, V.A. Geyler: Scattering on compact manifolds with infinitely thin horns, J. Math. Phys. 44 (2003), 371–405.MATHADSMathSciNetCrossRefGoogle Scholar

J. Brüning, V.A. Geyler, V.A. Margulis, M.A. Pyataev: Ballistic conductance of a quantum sphere, J. Phys. A35 (2002), 4239–4247.ADSGoogle Scholar

J. Brüning, V. Geyler, K. Pankrashkin: Cantor and band spectra for periodic quantum graphs with magnetic fields, Commun. Math. Phys. 269 (2007), 87–105.MATHADSCrossRefGoogle Scholar

D.C. Brydges, J. Fröhlich, A. Sokal: A new proof of existence and nontriviality of the continuum Φ⁴ ₂ and Φ⁴ ₃ quantum field theories, Commun. Math. Phys. 91 (1983), 141–186.ADSCrossRefGoogle Scholar

E.N. Bulgakov, P. Exner, K.N. Pichugin, A.F. Sadreev: Multiple bound states in scissor—shaped waveguides, Phys. Rev. B66 (2002), 155109ADSGoogle Scholar

W. Bulla, F. Gesztesy, W. Renger, B. Simon: Weakly coupled bound states in quantum waveguides, Proc. Amer. Math. Soc. 127 (1997), 1487–1495.MathSciNetCrossRefGoogle Scholar

W. Bulla, T. Trenkler: The free Dirac operator on compact and non—compact graphs, J. Math. Phys. 31 (1990), 1157–1163.MATHADSMathSciNetCrossRefGoogle Scholar

L.J. Bunce, J.D.M. Wright: Quantum measures and states on Jordan algebras, Commun. Math. Phys. 98 (1985), 187–202.MATHADSMathSciNetCrossRefGoogle Scholar

V.S. Buslaev, L. Dmitrieva: Bloch electrons in an external electric field, Leningrad Math. J. 1 (1991), 287–320.MathSciNetGoogle Scholar

M. Büttiker: Small normal—metal loop coupled to an electron reservoir, Phys. Rev. B32 (1985), 1846–1849.ADSGoogle Scholar

M. Büttiker: Absence of backscattering in the quantum Hall effect in multiprobeconductors, Phys. Rev. B38 (1988), 9375–9389.ADSGoogle Scholar

C. Cacciapuoti, P. Exner: Nontrivial edge coupling from a Dirichlet networksqueezing: the case of a bent waveguide, J. Phys. A40 (2007), F511–F523.ADSMathSciNetGoogle Scholar

J.W. Calkin: Two—sided ideals and congruence in the ring of bounded operators in Hilbert space, Ann. Math. 42 (1941), 839–873.MathSciNetCrossRefGoogle Scholar

F. Calogero: Upper and lower limits for the number of bound states in a given central potential, Commun. Math. Phys. 1 (1965), 80–88.MATHADSMathSciNetCrossRefGoogle Scholar

R.H. Cameron: A family of integrals serving to connect the Wiener Feynman integrals,J. Math. Phys. 39 (1961), 126–141.Google Scholar

R.H. Cameron: The Ilstow and Feynman integrals, J d'Analyse Math. 10(1962–63), 287–361.Google Scholar

R.H. Cameron: Approximation to certain Feynman integrals, J. d'Analyse Math. 21 (1968), 337–371.MATHGoogle Scholar

J.P. Carini, J.T. Londergan, K. Mullen, D.P. Murdock: Bound states and resonances in quantum wires, Phys. Rev. B46 (1992), 15538–15541.ADSGoogle Scholar

J.P. Carini, J.T. Londergan, K. Mullen, D.P. Murdock: Multiple bound states in sharply bent waveguides, Phys. Rev. B48 (1993), 4503–4514.ADSGoogle Scholar

J.P. Carini, J.T. Londergan, D.P. Murdock, D. Trinkle, C.S. Yung: Bound states in waveguides and bent quantum wires, I. Applications to waveguide systems, II. Electrons in quantum wires, Phys. Rev. B55 (1997), 9842–9851, 9852–9859.ADSGoogle Scholar

R. Carmona, W.Ch. Masters, B. Simon: Relativistic Schrodinger operators, J. Funct. Anal. 91 (1990), 117–142.MATHMathSciNetCrossRefGoogle Scholar

G. Carron, P. Exner, D. Krejčiřík: Topologically non—trivial quantum layers, J. Math. Phys. 45 (2004), 774–784.MATHADSMathSciNetCrossRefGoogle Scholar

G. Casati, I. Guarneri: Non—recurrent behaviour in quantum dynamics, Commun. Math. Phys. 95 (1984), 121–127.MATHADSMathSciNetCrossRefGoogle Scholar

D. Castrigiano, U. Mutze: On the commutant of an irreducible set of operators in a real Hilbert space, J. Math. Phys. 26 (1985), 1107–1110.MATHADSMathSciNetCrossRefGoogle Scholar

I. Catto, P. Exner, Ch. Hainzl: Enhanced binding revisited for a spinless particle in non-relativistic QED, J. Math. Phys. 45 (2004), 4174–4185.MATHADSMathSciNetCrossRefGoogle Scholar

K. Chadan, Ch. DeMol: Sufficient conditions for the existence of bound states in a potential without a spherical symmetry, Ann. Phys. 129 (1980), 466–478.MATHADSMathSciNetCrossRefGoogle Scholar

V. Chandrasekhar, M.J. Rooks, S. Wind, D.E. Prober: Observation of Aharonov-Bohm electron interference effects with periods h/e and h/2e in individual micron-size, normal-metal rings, Phys. Rev. Lett. 55 (1985), 1610–1613.ADSCrossRefGoogle Scholar

T. Chen, V. Vougalter, S. Vugalter: The increase of binding energy and enhanced binding in nonrelativistic QED, J. Math. Phys. 44 (2003), 1961–1970.MATHADSMathSciNetCrossRefGoogle Scholar

P. Chenaud, P. Duclos, P. Freitas, D. Krejčiřík: Geometrically induced discrete spectrum in curved tubes, Diff. Geom. Appl. 23 (2005), 95–105.MATHCrossRefGoogle Scholar

T. Cheon, P. Exner: An approximation to δ' couplings on graphs, J. Phys. A37 (2004), L329–335.ADSMathSciNetGoogle Scholar

T. Cheon, T. Shigehara: Realizing discontinuous wave functions with renor-malized short-range potentials, Phys. Lett. A243 (1998), 111–116.ADSGoogle Scholar

S. Cheremshantsev: Hamiltonians with zero—range interactions supported by a Brownian path, Ann. Inst. H. Poincaré: Phys. Théor. 56 (1992), 1–25.MATHMathSciNetGoogle Scholar

P.R. Chernoff: A note on product formulas for operators, J. Funct. Anal. 2 (1968), 238–242.MATHMathSciNetCrossRefGoogle Scholar

P.R. Chernoff, R.Hughes: A new class of point interactions in one dimension, J. Funct. Anal. 111(1993), 97–117.MATHMathSciNetCrossRefGoogle Scholar

L. Chetouani, F.F. Hamman: Coulomb's Green function in an n—dimensional Euclidean space, J. Math. Phys. 27 (1986), 2944–2948.MATHADSMathSciNetCrossRefGoogle Scholar

L. Chetouani, A. Chouchaoui, T.F. Hamman: Path integral solution for the Coulomb plus sector potential, Phys. Lett. A161 (1991), 87–97.ADSGoogle Scholar

Y. Colin de Verdière: Bohr—Sommerfeld rules to all orders, Ann. H. Poincaré 6 (2005), 925–936.MATHCrossRefGoogle Scholar

Ph. Combe, G. Rideau, R. Rodriguez, M. Sirugue—Collin: On the cylindrical approximation to certain Feynman integrals, Rep. Math. Phys. 13(1978), 279–294.MATHMathSciNetCrossRefADSGoogle Scholar

J.—M. Combes, P. Duclos, R. Seiler: Krein's formula and one—dimensional multiple well, J. Funct. Anal. 52 (1983), 257–301.MATHMathSciNetCrossRefGoogle Scholar

J.—M. Combes, P. Duclos, M. Klein, R. Seiler: The shape resonance, Commun. Math. Phys. 110 (1987), 215–236.MATHADSMathSciNetCrossRefGoogle Scholar

J.—M. Combes, P.D. Hislop: Stark ladder resonances for small electric fields, Commun. Math. Phys. 140 (1991), 291–320.MATHADSMathSciNetCrossRefGoogle Scholar

M. Combescure: Spectral properties of periodically kicked quantum Hamiltonians, J. Stat. Phys. 59 (1990), 679–690.MATHADSMathSciNetCrossRefGoogle Scholar

J. Conlon: The ground state of a Bose gas with Coulomb interaction I, II, Commun. Math. Phys. 100 (1985), 355–379; 108 (1987), 363–374.ADSMathSciNetCrossRefGoogle Scholar

J.G. Conlon, E.H. Lieb, H.—T. Yau: The N ^7/5 law for charged bosons, Commun. Math. Phys. 116 (1988), 417–488.ADSMathSciNetCrossRefGoogle Scholar

A. Connes: The Tomita—Takesaki theory and classification of type III factors, in the proceedings volume [[ Kas ]], pp. 29–46.Google Scholar

J.M. Cook: The mathematics of second quantization, Trans. Am. Math. Soc. 74 (1953), 222–245.MATHCrossRefGoogle Scholar

J.M. Cook: Convergence of the Møller wave matrix, J. Math. Phys. 36 (1957), 82–87.Google Scholar

H. Cornean, A. Jensen, V. Moldoveanu: A rigorous proof for the Landauer-Büttiker formula, J. Math. Phys. 46 (2005), 042106.ADSMathSciNetCrossRefGoogle Scholar

F.A.B. Coutinho, C.P. Malta, J. Fernando Perez: Sufficient conditions for the existence of bound states of N particles with attractive potentials, Phys. Lett. 100A (1984), 460–462.ADSMathSciNetGoogle Scholar

E. Christensen: Measures on projections and physical states, Commun. Math. Phys. 86 (1982), 529–538.MATHADSMathSciNetCrossRefGoogle Scholar

R.E. Crandall: Exact propagator for reflectionless potentials, J. Phys. A16 (1983), 3005–3011.ADSMathSciNetGoogle Scholar

M. Cwikel: Weak type estimates for singular values and the number of bound states of Schrödinger operators, Ann. Math. 106 (1977), 93–100.MathSciNetCrossRefGoogle Scholar

H.L. Cycon: Resonances defined by modified dilations, Helv. Phys. Acta 58 (1985), 969–981.MathSciNetGoogle Scholar

I. Daubechies, E.H. Lieb: One electron relativistic molecule with Coulomb interaction, Commun. Math. Phys. 90 (1983), 497–510.MATHADSMathSciNetCrossRefGoogle Scholar

G. Dell'Antonio, L. Tenuta: Quantum graphs as holonomic constraints, J. Math. Phys. 47 (2006), 072102.ADSMathSciNetCrossRefGoogle Scholar

M. Demuth: Pole approximation and spectral concentration, Math. Nachr. 73 (1976), 65–72.MATHMathSciNetCrossRefGoogle Scholar

J. Derezyński: A new proof of the propagation theorem for N-body quantum systems, Commun. Math. Phys. 122 (1989), 203-231.ADSCrossRefGoogle Scholar

J. Derezyński: Algebraic approach to the N —body long—range scattering, Rep. Math. Phys. 3 (1991), 1–62.CrossRefGoogle Scholar

C. DeWitt, S.G. Low, L.S. Schulman, A.Y. Shiekh: Wedges I, Found. Phys. 16 (1986), 311–349.ADSMathSciNetCrossRefGoogle Scholar

C. DeWitt—Morette: The semiclassical expansion, Ann. Phys. 97 (1976), 367–399; 101, 682–683.ADSMathSciNetCrossRefGoogle Scholar

C. DeWitt—Morette, A. Maheswari, B. Nelson: Path—integration in nonrelativistic quantum mechanics, Phys. Rep. 50 (1979), 255–372.ADSMathSciNetCrossRefGoogle Scholar

J. Dittrich, P. Exner: Tunneling through a singular potential barrier, J. Math.Phys. 26 (1985), 2000–2008.MATHADSMathSciNetCrossRefGoogle Scholar

J. Dittrich, P. Exner: A non—relativistic model of two—particle decay I–IV, Czech. J. Phys. B37 (1987), 503–515, 1028–1034; B38 (1988), 591–610; B39 (1989), 121–138.ADSMathSciNetCrossRefGoogle Scholar

J. Dittrich, P. Exner, P. Seba: Dirac operators with a spherically symmetric δ—shell interaction, J. Math. Phys. 30 (1989), 2975–2982.MathSciNetCrossRefGoogle Scholar

J. Dittrich, P. Exner, P. Seba: Dirac Hamiltonians with Coulombic potential and spherically symmetric shell contact interaction, J. Math. Phys. 33 (1992), 2207–2214.MATHADSMathSciNetCrossRefGoogle Scholar

J. Dittrich, J. Kříž: Curved planar quantum wires with Dirichlet and Neumann boundary conditions, J. Phys. A35 (2002), L269–275.ADSGoogle Scholar

J. Dittrich, J. Kříž: Bound states in straight quantum waveguides with combined boundary conditions, J. Math. Phys. 43 (2002), 3892–3915.MATHADSMathSciNetCrossRefGoogle Scholar

J. Dixmier: Sur la relation i(PQ-QP) = I, Compos. Math. 13 (1956), 263–269.MathSciNetGoogle Scholar

J.D. Dollard, C.N. Friedmann: Existence and completeness of the Møller wave operators for radial potentials satisfying\(\int_0^1 {\left. r \right|} v\left( r \right)\left| {dr} \right. + \int_1^\infty {\left| v \right.\left( r \right)} \,\left| {dr} \right.\, < \infty \), J. Math. Phys. 21 (1980), 1336–1339.Google Scholar

E. Doron, U. Smilansky: Chaotic spectroscopy, Phys. Rev. Lett. 68 (1992), 1255–1258.ADSCrossRefGoogle Scholar

T. Drisch: Generalization of Gleason's theorem, Int. J. Theor. Phys. 18 (1978), 239–243.MathSciNetCrossRefGoogle Scholar

P. Duclos, P. Exner: Curvature—induced bound states in quantum waveguides in two and three dimensions, Rev. Math. Phys. 7 (1995), 73–102.MATHMathSciNetCrossRefGoogle Scholar

P. Duclos, P. Exner, D. Krejčiřík: Bound states in curved quantum layers, Commun. Math. Phys. 223 (2001), 13–28.MATHADSCrossRefGoogle Scholar

P. Duclos, P. Exner, B. Meller: Exponential bounds on curvature—induced resonances in a two-dimensional Dirichlet tube, Helv. Phys. Acta 71 (1998), 133–162.MATHMathSciNetGoogle Scholar

P. Duclos, P. Exner, B. Meller: Open quantum dots: resonances from perturbed symmetry and bound states in strong magnetic fields, Rep. Math. Phys. 47 (2001), 253–267.MATHMathSciNetCrossRefADSGoogle Scholar

P. Duclos, P. Exner, P. Š̌tovíček: Curvature—induced resonances in a two—dimensional Dirichlet tube, Ann.Inst. H.Poincaré: Phys. Théor. 62 (1995), 81–101.MATHGoogle Scholar

P. Duclos, P. Š̌tovíček: Floquet Hamiltonians with pure spectrum, Commun. Math. Phys. 177 (1996), 327–347.MATHADSCrossRefGoogle Scholar

P. Duclos, P. Š̌tovíček, M. Vittot: Perturbations of an eigen-value from a dense point spectrum: a general Floquet Hamiltonian, Ann. Inst. H. Poincaré 71 (1999), 241–301.MATHGoogle Scholar

I.H. Duru: Quantum treatment of a class of time—dependent potentials, J. Phys. A22 (1989), 4827–4833.ADSMathSciNetGoogle Scholar

J.—P. Eckmann, Ph.C. Zabey: Impossibility of quantum mechanics in a Hilbert space over a finite field, Helv. Phys. Acta 42 (1969), 420–424.MathSciNetGoogle Scholar

M. Eilers, M. Horst: The theorem of Gleason for nonseparable Hilbert spaces, Int. J. Theor. Phys. 13 (1975), 419–424.MathSciNetCrossRefGoogle Scholar

T. Ekholm, H. Kovařík: Stability of the magnetic Schrödinger operator in a waveguide, Comm. PDE 30 (2005), 539–565.MATHGoogle Scholar

K.D. Elworthy, A. Truman: A Cameron—Martin formula for Feynman integrals (the origin of Maslov indices), in Mathematical Problems in Theoretical Physics, Lecture Notes in Physics, vol. 153, Springer, Berlin 1982; pp. 288–294.Google Scholar

G.G. Emch: Mécanique quantique quaternionique et relativité restreinte I, II, Helv. Phys. Acta 36 (1963), 739–769, 770–788.MathSciNetGoogle Scholar

G.G. Emch, K.B. Sinha: Weak quantization in a non—perturbative model, J. Math. Phys. 20 (1979), 1336–1340.ADSMathSciNetCrossRefGoogle Scholar

V. Enss: Asymptotic completeness for quantum—mechanical potential scattering, I. Short—range potentials, II. Singular and long—range potentials, Commun. Math. Phys. 61 (1978), 285–291; Ann. Phys. 119 (1979), 117–132.MATHADSMathSciNetCrossRefGoogle Scholar

V. Enss: Topics in scattering theory for multiparticle systems: a progress report, Physica A124 (1984), 269–292.ADSMathSciNetGoogle Scholar

V. Enss, K. Veselič: Bound states and propagating states for time dependent Hamiltonians, Ann. Inst. H. Poincaré: Phys. Théor. 39 (1983), 159–191.MATHGoogle Scholar

G. Epifanio: On the matrix representation of unbounded operators, J. Math. Phys. 17 (1976), 1688–1691.MATHADSMathSciNetCrossRefGoogle Scholar

G. Epifanio, C. Trapani: Remarks on a theorem by G. Epifanio, J. Math. Phys. 20 (1979), 1673–1675.MATHADSMathSciNetCrossRefGoogle Scholar

G. Epifanio, C. Trapani: Some spectral properties in algebras of unbounded operators, J. Math. Phys. 22 (1981), 974–978.MATHADSMathSciNetCrossRefGoogle Scholar

G. Epifanio, C. Trapani: V *—algebras: a particular class of unbounded operator algebras, J. Math. Phys. 25 (1985), 2633–2637.ADSMathSciNetCrossRefGoogle Scholar

W.D. Evans, R.T. Lewis, Y. Saito: Some geometric spectral properties of N—body Schrödinger operators, Arch. Rat. Mech. Anal. 113 (1991), 377–400.MATHMathSciNetCrossRefGoogle Scholar

P. Exner: Bounded—energy approximation to an unstable quantum system, Rep. Math. Phys. 17 (1980), 275–285.MATHMathSciNetCrossRefADSGoogle Scholar

P. Exner: Generalized Bargmann inequalities, Rep. Math. Phys. 19 (1984), 249–255.MATHMathSciNetCrossRefADSGoogle Scholar

P. Exner: Representations of the Poincare group associated with unstable articles, Phys. Rev. D28 (1983), 3621–2627.ADSMathSciNetGoogle Scholar

P. Exner: Remark on the energy spectrum of a decaying system, Commun. Math. Phys. 50 (1976), 1–10.ADSMathSciNetCrossRefGoogle Scholar

P. Exner: One more theorem on the short—time regeneration rate, J. Math. Phys. 30 (1989), 2563–2564.MATHADSMathSciNetCrossRefGoogle Scholar

P. Exner: A solvable model of two—channel scattering, Helv. Phys. Acta 64 (1991), 592–609.MathSciNetGoogle Scholar

P. Exner: A model of resonance scattering on curved quantum wires, Ann. Physik 47 (1990), 123–138.ADSMathSciNetCrossRefGoogle Scholar

P. Exner: The absence of the absolutely continuous spectrum for δ' Wannier—Stark ladders, J. Math. Phys. 36 (1995), 4561–4570.MATHADSMathSciNetCrossRefGoogle Scholar

P. Exner: Lattice Kronig—Penney models, Phys. Rev. Lett. 74 (1995), 3503–3506.ADSCrossRefGoogle Scholar

P. Exner: Contact interactions on graph superlattices, J. Phys. A29 (1996), 87–102.ADSMathSciNetGoogle Scholar

P. Exner: Weakly coupled states on branching graphs, Lett. Math. Phys. 38 (1996), 313–320.Ex 12 ] P. Exner: A duality between Schrodinger operators on graphs and certain Jacobi matrices, Ann. Inst. H. Poincare: Phys. Theor. 66 (1997), 359–371.MATHADSMathSciNetCrossRefGoogle Scholar

P. Exner: A duality between Schrodinger operators on graphs and certain Jacobi matrices, Ann. Inst. H. Poincare: Phys. Theor. 66 (1997), 359–371.MATHMathSciNetGoogle Scholar

P. Exner: Magnetoresonances on a lasso graph, Found. Phys. 27 (1997), 171–190.ExADSMathSciNetCrossRefGoogle Scholar

P. Exner: Point interactions in a tube, in “Stochastic Processes: Physics andGeometry: New Interplayes II” (A volume in honor of S. Albeverio; F. Gesztesy et al., eds.); CMS Conference Proceedings, vol. 29, Providence, R.I. 2000; pp. 165– 174Google Scholar

P. Exner: Leaky quantum graphs: a review, in the proceedings volume [EKKST]; arXiv: 0710.5903 [math-ph]Google Scholar

P. Exner: An isoperimetric problem for leaky loops and related mean-chord nequalities, J. Math. Phys. 46 (2005), 062105Google Scholar

P. Exner: Necklaces with interacting beads: isoperimetric problems, AMS “Contemporary Math” Series, vol. 412, Providence, RI, 2003; pp. 141–149.MathSciNetGoogle Scholar

P. Exner, M. Fraas: The decay law can have an irregular character, J. Phys. A40 (2007), 1333–1340.ADSMathSciNetGoogle Scholar

P. Exner, P. Freitas, D. Krejčiřík: A lower bound to the spectral threshold in curved tubes, Proc. Roy. Soc. A460 (2004), 3457–3467.ADSMathSciNetGoogle Scholar

P. Exner, R. Gawlista: Band spectra of rectangular graph superlattices, Phys. Rev. B53 (1996), 7275–7286.ADSGoogle Scholar

P. Exner, R. Gawlista, P. Seba, M. Tater: Point interactions in a strip, Ann. Phys. 252 (1996), 133–179.MATHADSMathSciNetCrossRefGoogle Scholar

P. Exner, E.M. Harrell, M. Loss: Optimal eigenvalues for some Laplacians and Schrodinger operators depending on curvature, Proceedings of the Conference “Mathematical Results in Quantum Mechanics”(QMath7, Prague 1998); Operator Theory: Advances and Applications, Birkhauser, Basel; pp. 47–53.Google Scholar

P. Exner, E.M. Harrell, M. Loss: Inequalities for means of chords, with appli cation to isoperimetric problems, Lett. Math. Phys. 75 (2006), 225–233; addendum 77 (2006), 219.Google Scholar

P. Exner, T. Ichinose: Geometrically induced spectrum in curved leaky wires, J. Phys. A34 (2001), 1439–1450.ADSMathSciNetGoogle Scholar

P. Exner, G.I. Kolerov: Uniform product formulae, with application to the Feynman—Nelson integral for open systems, Lett. Math. Phys. 6 (1982), 151–159.ADSGoogle Scholar

P. Exner, D. Krejčiřík: Quantum waveguide with a lateral semitransparent barrier: spectral and scattering properties, J. Phys. A32 (1999), 4475–4494.ADSMathSciNetGoogle Scholar

P. Exner, D. Krejčiřík: Bound states in mildly curved layers, J. Phys. A34 (2001), 5969–5985.ADSMathSciNetGoogle Scholar

P. Exner, H. Linde, T. Weidl: Lieb–Thirring inequalities for geometrically induced bound states, Lett. Math. Phys. 70 (2004), 83–95.MATHADSMathSciNetCrossRefGoogle Scholar

P. Exner, H. Neidhardt, V.A. Zagrebnov: Potential approximations to δ': an inverse Klauder phenomenon with norm-resolvent convergence, Commun. Math. Phys. 224 (2001), 593–612.ADSMathSciNetCrossRefGoogle Scholar

P. Exner, K. Nemcova: Quantum mechanics of layers with a finite number of point perturbations, J. Math. Phys. 43 (2002), 1152–1184.MATHADSMathSciNetCrossRefGoogle Scholar

P. Exner, K. Nemcova: Magnetic layers with periodic point perturbations, Rep. Math. Phys. 52 (2003), 255–280.MATHMathSciNetCrossRefADSGoogle Scholar

P. Exner, O. Post: Convergence of spectra of graph—like thin manifolds, J. Geom. Phys. 54 (2005), 77–115.MATHADSMathSciNetCrossRefGoogle Scholar

P. Exner, O. Post: Convergence of resonances on thin branched quantum wave guides, J. Math. Phys. 48 (2007), 092104ADSMathSciNetCrossRefGoogle Scholar

P. Exner, P. Šeba: Bound states in curved quantum waveguides, J. Math. Phys. 30 (1989), 2574–2580.MATHADSMathSciNetCrossRefGoogle Scholar

P. Exner, P. Šeba: Electrons in semiconductor microstructures: a challenge to operator theorists, in the proceedings volume [[ EŠ 2 ]], pp. 79–100.Google Scholar

P. Exner, P. Šeba: Quantum motion in two planes connected at one point, Lett. Math. Phys. 12 (1986), 193–198.MATHADSMathSciNetCrossRefGoogle Scholar

P. Exner, P. Šeba: Quantum motion on a halfline connected to a plane, J. Math. Phys. 28 (1987), 386–391, 2254.ADSGoogle Scholar

P. Exner, P. Šeba: Schrödinger operators on unusual manifolds, in the proceed ings volume [[AFHL]], pp. 227–253.Google Scholar

P. Exner, P. Seba: Free quantum motion on a branching graph, Rep. Math. Phys. 28 (1989), 7–26.MATHMathSciNetCrossRefADSGoogle Scholar

P. Exner, P. Šeba: Trapping modes in a curved electromagnetic waveguide with perfectly conducting walls, Phys. Lett. A144 (1990), 347–350.ADSMathSciNetGoogle Scholar

EŠ 8] P. Exner, P. Šeba: A “hybrid plane” with spin-orbit interaction, Russ. J. Math. Phys. 14 (2007), 401–405.CrossRefGoogle Scholar

P. Exner, P. Šeba: Resonance statistics in a microwave cavity with a thin antenna, Phys. Lett. A228 (1997), 146–150.ADSGoogle Scholar

P. Exner, P. Šeba, P. Š̌tovířek: On existence of a bound state in an L-shaped waveguide, Czech. J. Phys. B39 (1989), 1181–1191.ADSCrossRefGoogle Scholar

P. Exner, P. Seba, P. Š̌tovířek: Semiconductor edges can bind electrons, Phys. Lett. A150 (1990), 179–182.ADSGoogle Scholar

P. Exner, P. Seba, P. Š̌tovířek: Quantum interference on graphs controlled by an external electric field, J. Phys. A21 (1988), 4009–4019.ADSGoogle Scholar

P. Exner, P. Šeba, M. Tater, D. Vaněk: Bound states and scattering in quantum waveguides coupled laterally through a boundary window, J. Math. Phys. 37 (1996), 4867–4887.MATHADSMathSciNetCrossRefGoogle Scholar

P. Exner, E. Šerešová: Appendix resonances on a simple graph, J. Phys. A27 (1994), 8269–8278.ADSGoogle Scholar

P. Exner, M. Tater, D. Vaněk: A single-mode quantum transport in serial—structure geometric scatterers, J. Math. Phys. 42(2001), 4050–4078.MATHADSMathSciNetCrossRefGoogle Scholar

P. Exner, O. Turek: Approximations of singular vertex couplings in quantum graphs, Rev. Math. Phys. 19 (2007), 571–606.MATHMathSciNetCrossRefGoogle Scholar

P. Exner, S.A. Vugalter: Bounds states in a locally deformed waveguide: the critical case, Lett. Math. Phys. 39 (1997), 59–68.MATHMathSciNetCrossRefGoogle Scholar

P. Exner, S.A. Vugalter: Asymptotic estimates for bound states in quantum waveguides coupled laterally through a narrow window, Ann. Inst. H. Poincarě: Phys. Theor. 65 (1996), 109–123.MATHMathSciNetGoogle Scholar

P. Exner, S.A. Vugalter: On the number of particles that a curved quantum waveguide can bind, J. Math. Phys. 40 (1999), 4630–4638.MATHADSMathSciNetCrossRefGoogle Scholar

P. Exner, K. Yoshitomi: Asymptotics of eigenvalues of the Schrodinger operator with a strong δ-interaction on a loop, J. Geom. Phys. 41 (2002), 344–358.MATHADSMathSciNetCrossRefGoogle Scholar

P. Exner, V.A. Zagrebnov: Bose-Einstein condensation in geometrically de formed tubes, J. Phys. A38 (2005), L463–470.ADSMathSciNetGoogle Scholar

W.G. Faris: Inequalities and uncertainty principles, J. Math. Phys. 19 (1978), 461–466.ADSMathSciNetCrossRefGoogle Scholar

W.G. Faris: Product formulas for perturbation of linear operators, J. Funct. Anal. 1 (1967), 93–107.MATHMathSciNetCrossRefGoogle Scholar

J. Feldmann, J. Magnen, V. Rivasseau, R. Seněor: A renormalizable field theory: the massive Gross—Neveu model in two dimensions, Commun. Math. Phys. 103 (1986), 67–103.ADSCrossRefGoogle Scholar

J.G.M. Fell: The dual spaces of c*—algebras, Trans. Am. Math. Soc. 94 (1960), 365–403.MATHMathSciNetCrossRefGoogle Scholar

R.P. Feynman: Space—time approach to nonrelativistic quantum mechanics, Rev. Mod. Phys. 20 (1948), 367–387.ADSMathSciNetCrossRefGoogle Scholar

D. Finkelstein, J.M. Jauch, S. Schminovich, D. Speiser: Foundations of quaternionic quantum mechanics, J. Math. Phys. 3 (1962), 207–220.ADSCrossRefGoogle Scholar

D. Finkelstein, J.M. Jauch, S. Schminovich, D. Speiser: Principle of general Q covariance, J. Math. Phys. 4 (1963), 788–796.MATHADSCrossRefGoogle Scholar

V.A. Fock: Konfigurationsraum und zweite Quantelung, Z. Phys. 75 (1932), 622–647.MATHADSCrossRefGoogle Scholar

K.O. Friedrichs: On the perturbation of continuous spectra, Commun. Appl. Math. 1 (1948), 361–406.MathSciNetGoogle Scholar

J. Frohlich, E.H. Lieb, M. Loss: Stability of Coulomb systems with magnetic fields, I. The one—electron atom, Commun. Math. Phys. 104 (1986), 251–270.ADSMathSciNetCrossRefGoogle Scholar

T. Fulop, I. Tsutsui: A free particle on a circle with point interaction, Phys. Lett. A264 (2000), 366–374.ADSMathSciNetGoogle Scholar

G. Gamow: Zur Quantetheorie des Atomkernes, Z. Phys. 51 (1928), 204–212.ADSCrossRefGoogle Scholar

K. Gawedzki, A. Kupiainen: Gross—Neveu model through convergent expan sions, Commun. Math. Phys. 102 (1985), 1–30.ADSMathSciNetCrossRefGoogle Scholar

I.M. Gel'fand, M.A. Naimark: On embedding of a normed ring to the ring of operators in Hilbert space, Mat. Sbornik 12 (1943), 197–213 (in Russian). Google Scholar

C. Gerard, A. Martinez, D. Robert: Breit—Wigner formulas for the scattering phase and the total cross section in the semiclassical limit, Commun. Math. Phys. 121 (1989), 323–336.MATHADSMathSciNetCrossRefGoogle Scholar

N.I. Gerasimenko, B.S. Pavlov: Scattering problem on non—compact graphs, Teor. mat. fiz. 74 (1988), 345–359 (in Russian). MathSciNetGoogle Scholar

F. Gesztesy, H. Grosse, B. Thaller: Efficient method for calculating relativistic corrections to spin 1/2 particles, Phys. Rev. Lett. 50 (1983), 625–628.ADSCrossRefGoogle Scholar

F. Gesztesy, H. Grosse, B. Thaller: First order relativistic corrections and the spectral concentration, Adv. Appl. Math. 6 (1985), 159–176.MATHMathSciNetCrossRefGoogle Scholar

F. Gesztesy, D. Gurarie, H. Holden, M. Klaus, L. Sadun, B. Simon, P. Vogel: Trapping and cascading in the large coupling limit, Commun. Math. Phys. 118 (1988), 597–634.MATHADSCrossRefGoogle Scholar

F. Gesztesy, P. Šeba: New analytically solvable models of relativistic point interactions, Lett. Math. Phys. 13 (1987), 213–225.CrossRefGoogle Scholar

F. Gesztesy, B. Simon, B. Thaller: On the self—adjointness of Dirac operator with anomalous magnetic moment, Proc. Am. Math. Soc. 94 (1985), 115–118.MATHMathSciNetCrossRefGoogle Scholar

V. Glaser, H. Grosse, A. Martin: Bounds on the number of eigenvalues of the Schrödinger operator, Commun. Math. Phys. 59 (1978), 197–212.MATHADSMathSciNetCrossRefGoogle Scholar

V. Glaser, A. Martin, H. Grosse, W. Thirring: A family of optimal condi tions for the absence of bound states in a potential, in [[ LSW ]], pp. 169–194.Google Scholar

R.J. Glauber: Photon correlations, Phys. Rev. Lett. 10 (1963), 84–86.ADSMathSciNetCrossRefGoogle Scholar

R.J. Glauber: Coherent and incoherent states of the radiation fields, Phys. Rev. 131 (1963), 2766–2788.ADSMathSciNetCrossRefGoogle Scholar

A.M. Gleason: Measures on the closed subspaces of a Hilbert space, J. Math. Mech. 6 (1957), 91–110.MathSciNetGoogle Scholar

J. Glimm, A. Jaffe: Boson quantum field models, in [[ Str ]], pp. 77–143.Google Scholar

J. Goldstone, R.L. Jaffe: Bound states in twisting tubes, Phys. Rev. B45 (1992), 14100–14107.ADSGoogle Scholar

C. Gordon, D.L. Webb, S. Wolpert: One cannot hear the shape of a drum, Bull. Am. Math. Soc. 27 (1992), 134–138.MATHMathSciNetCrossRefGoogle Scholar

G.M. Graf: Asymptotic completeness for N—body short range quantum sys tems: a new proof, Commun. Math. Phys. 132 (1990), 73–101.MATHADSMathSciNetCrossRefGoogle Scholar

S. Graffi, V. Grecchi: Resonances in Stark effect of atomic systems, Commun. Math. Phys. 79 (1981), 91–110.MATHADSMathSciNetCrossRefGoogle Scholar

M. Griesemer, E.H. Lieb, M. Loss: Ground states in non-relativistic quantum electrodynamics, Invent. Math. 145 (2001), 557–595.MATHADSMathSciNetCrossRefGoogle Scholar

D. Grieser: Spectra of graph neighborhoods and scattering, arXiv:0710.3405v1 [math.SP]Google Scholar

D. Gromoll, W. Meyer, On complete open manifolds of positive curvature, Ann. Math. 90 (1969), 75–90.MathSciNetCrossRefGoogle Scholar

C. Grosche: Coulomb potentials by path integration, Fortschr. Phys. 40 (1992), 695–737.MathSciNetCrossRefGoogle Scholar

H. Grosse: On the level order for Dirac operators, Phys. Lett. B197 (1987), 413–417.ADSMathSciNetGoogle Scholar

S.P. Gudder: The Hilbert space axiom in quantum mechanics, in Old and New Questions in Physics, Cosmology, Philosophy and Theoretical Biology. Essays in Honor of W. Yourgrau, Plenum Press, New York 1983; pp. 109–127.Google Scholar

R. Haag: Quantum field theory, in the proceedings volume [[ Str ]], pp. 1–16.Google Scholar

R. Haag: On quantum field theories, Danske Vid. Selsk. Mat.—Fys. Medd. 29 (1955), No. 12.Google Scholar

R. Haag: Local relativistic quantum physics, Physica A124(1984), 357–364.ADSMathSciNetGoogle Scholar

R. Haag, D. Kastler: An algebraic approach to quantum field theory, J. Math. Phys. 5 (1964), 848–861.MATHADSMathSciNetCrossRefGoogle Scholar

M. Hack: On the convergence to the Møller wave operators, Nuovo Cimento 9 (1958), 731–733.MATHCrossRefGoogle Scholar

G. Hagedorn: Semiclassical quantum mechanics I—IV, Commun. Math. Phys. 71 (1980), 77–93; Ann. Phys. 135 (1981), 58–70; Ann. Inst. H. Poincaré A42 (1985), 363–374.Google Scholar

G. Hagedorn: Adiabatic expansions near adiabatic crossings, Ann. Phys. 196 (1989), 278–295.MATHADSMathSciNetCrossRefGoogle Scholar

G. Hagedorn, A. Joye: Molecular propagation through small avoided crossings of electron energy levels, Rev. Math. Phys. 11 (1999), 41–101.MATHMathSciNetCrossRefGoogle Scholar

G. Hagedorn, A. Joye: Time development of exponentially small non-adiabatic transitions, Commun. Math. Phys. 250 (2004), 393–413.MATHADSMathSciNetCrossRefGoogle Scholar

G. Hagedorn, M. Loss, J. Slawny: Non—stochasticity of time—dependent quadratic Hamiltonians and the spectra of transformation, J. Phys. A19 (1986), 521–531.ADSMathSciNetGoogle Scholar

Ch. Hainzl, R. Seiringer: Mass renormalization and energy level shift in non-relativistic QED, Adv. Theor. Math. Phys. 6 (2002), 847–871.MathSciNetGoogle Scholar

G.H. Hardy: A note on a Theorem by Hilbert, Math. Z. 6 (1920), 314–317.MathSciNetCrossRefGoogle Scholar

M. Harmer: Hermitian symplectic geometry and extension theory, J. Phys. A33 (2000), 9193–9203.ADSMathSciNetGoogle Scholar

P.G. Harper: Single band motion of conduction electrons in a uniform mag netic field, Proc. Roy. Soc. London A68 (1955), 874–878.Google Scholar

M. Havlíček, P. Exner: Note on the description of an unstable system, Czech. J. Phys. B19 (1973), 594–600.Google Scholar

R. Hempel, L.A. Seco, B. Simon: The essential spectrum of Neumann Lapla- cians on some bounded singular domains, J. Funct. Anal. 102 (1991), 448–483.MATHMathSciNetCrossRefGoogle Scholar

K. Hepp: The classical limit for quantum correlation function, Commun. Math. Phys. 35 (1974), 265–277.ADSMathSciNetCrossRefGoogle Scholar

I.W. Herbst: Dilation analycity in constant electric field, I. The two—body problem, Commun. Math. Phys. 64 (1979), 279–298.MATHADSMathSciNetGoogle Scholar

I.W. Herbst, J.S. Howland: The Stark ladder resonances and other one—dimen sional external field problems, Commun. Math. Phys. 80 (1981), 23–42.MATHADSMathSciNetCrossRefGoogle Scholar

F. Herbut: Characterization of compatibility, comparability and orthogonality of quantum propositions in terms of chains of filters, J. Phys. A18 (1985), 2901–2907.ADSMathSciNetGoogle Scholar

J. Hilgevoord, J.B.M. Uffink: Overall width, mean peak width and uncertainty principle, Phys. Lett. 95A (1983), 474–476.ADSGoogle Scholar

R.N. Hill: Proof that the H_- ion has only one bound state, Phys. Rev. Lett. 38 (1977), 643–646.ADSCrossRefGoogle Scholar

F. Hiroshima, H. Spohn: Enhanced binding through coupling to a quantum field, Ann. Henri Poincaré 2 (2001), 1159–1187.MATHMathSciNetCrossRefGoogle Scholar

G. Hofmann: On the existence of quantum fields in space—time dimension 4, Rep. Math. Phys. 18 (1980), 231–242.MATHMathSciNetCrossRefADSGoogle Scholar

R. Hofstadter: Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields, Phys. Rev. B14 (1976), 2239–2249.ADSGoogle Scholar

G. Höhler: Über die Exponentialnäherung beim Teilchenzerfall, Z. Phys. 152 (1958), 546–565.MATHADSCrossRefGoogle Scholar

S.S. Horužii, A.V. Voronin: Field algebras do not leave field domains invariant, Commun. Math. Phys. 102 (1986), 687–692.ADSCrossRefGoogle Scholar

L.P. Horwitz, L.C. Biedenharn: Quaternion quantum mechanics: second quan tization and gauge fields, Ann. Phys. 157 (1984), 432–488.MATHADSMathSciNetCrossRefGoogle Scholar

L.P. Horwitz, J.A. LaVita, J.-P. Marchand: The inverse decay problem, J. Math. Phys. 12 (1971), 2537–2543.MATHADSMathSciNetCrossRefGoogle Scholar

L.P. Horwitz, J. Levitan: A soluble model for time dependent perturbation of an unstable quantum system, Phys. Lett. A153 (1991), 413–419.ADSMathSciNetGoogle Scholar

L.P. Horwitz. J.-P. Marchand: The decay-scattering system, Rocky Mts. J. Math. 1 (1971), 225–253.MathSciNetGoogle Scholar

L. van Hove: Sur le probleme des relations entre les transformations unitaires de la Mécanique quantique et les transformations canoniques de la Mécanique classique, Bull. Acad. Roy. de Belgique, Classe des Sciences 37 (1951), 610–620.Google Scholar

J.S. Howland: Perturbations of embedded eigenvalues by operators of finite rank, J. Math. Anal. Appl. 23 (1968), 575–584.MATHMathSciNetCrossRefGoogle Scholar

J.S. Howland: Spectral concentration and virtual poles I, II, Am. J. Math. 91 (1969), 1106–1126; Trans. Am. Math. Soc. 162 (1971), 141–156.MATHMathSciNetCrossRefGoogle Scholar

J.S. Howland: Puiseaux series for resonances at an embedded eigenvalue, Pacific J. Math. 55 (1974), 157–176.MATHMathSciNetGoogle Scholar

J.S. Howland: The Livsic matrix in perturbation theory, J. Math. Anal. Appl. 50 (1975), 415–437.MATHMathSciNetCrossRefGoogle Scholar

J.S. Howland: Stationary theory for time—dependent Hamiltonians, Math. Ann. 207 (1974), 315–333.MATHMathSciNetCrossRefGoogle Scholar

J.S. Howland: Floquet operator with singular spectrum I, II, Ann. Inst. H. Poincarée: Phys.Théor. 49 (1989), 309–323, 325–335.MathSciNetGoogle Scholar

J.S. Howland: Stability of quantum oscillators, J. Phys. A25 (1992), 5177–81.ADSMathSciNetGoogle Scholar

D. Hundertmark, E.H. Lieb, L.E. Thomas: A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator, Adv. Theor. Math. Phys. 2(1998), 719–731.MATHMathSciNetGoogle Scholar

D. Hundertmark, A. Laptev, T. Weidl: New bounds on the Lieb-Thirring constants, Invent. Math. 140 (2000), 693–704.MATHADSMathSciNetCrossRefGoogle Scholar

W. Hunziker: Resonances, metastable states and exponential decay laws in perturbation theory, Commun. Math. Phys. 132 (1990), 177–188.MATHADSMathSciNetCrossRefGoogle Scholar

T. Ichinose: Path integral for a hyperbolic system of the first order, Duke Math. J. 51 (1984), 1–36.MATHMathSciNetCrossRefGoogle Scholar

T. Ikebe, T. Kato: Uniqueness of the self—adjoint extension of singular elliptic differential operators, Arch. Rat. Mech. Anal. 9 (1962), 77–92.MATHMathSciNetCrossRefGoogle Scholar

K. Ito: Wiener integral and Feynman integral, in Proceedings of the 4th Berke ley Symposium on Mathematical Statistics and Probability, vol. 2, University of California Press, Berkeley, CA 1961; pp. 227–238.Google Scholar

K. Ito: Generalized uniform complex measures in the Hilbertian metric space with their applications to the Feynman integral, in Proceedings of the 5th Berke ley Symposium on Mathematical Statistics and Probability, vol.2/1, University of California Press, Berkeley, CA 1967; pp. 145–167.Google Scholar

P.A. Ivert, T. Sjödin: On the impossibility of a finite proposition lattice for quantum mechanics, Helv. Phys. Acta 51 (1978), 635–636.MathSciNetGoogle Scholar

J.M. Jauch: Theory of the scattering operator I, II, Helv. Phys.Acta 31 (1958), 127–158, 661–684.MATHMathSciNetGoogle Scholar

J.M. Jauch, C. Piron: Can hidden variables be excluded in quantum mechanics?, Helv. Phys. Acta 36 (1963), 827–837.MATHMathSciNetGoogle Scholar

H. Jauslin, J.L. Lebowitz: Spectral and stability aspects of quantum chaos, Chaos 1 (1991), 114–121.MATHADSMathSciNetCrossRefGoogle Scholar

G.W. Johnson: The equivalence of two approaches to the Feynman integral, J. Math. Phys. 23 (1982), 2090–2096.MATHADSMathSciNetCrossRefGoogle Scholar

G.W. Johnson: Feynman's paper revisited, Suppl. Rend. Circ. Mat. Palermo, Ser.II, 17 (1987), 249–270.Google Scholar

G.W. Johnson, D.L. Skoug: A Banach algebra of Feynman integrable functions with applications to an integral equation which is formally equivalent to Schrödinger equation, J. Funct. Anal. 12 (1973), 129–152.MATHMathSciNetCrossRefGoogle Scholar

P. Jordan, J. von Neumann, E. Wigner: On an algebraic generalization of the quantum mechanical formalism, Ann. Math. 35 (1934), 29–64.CrossRefGoogle Scholar

R. Jost, A. Pais: On the scattering of a particle by a static potential, Phys. Rev. 82 (1951), 840–850.MATHADSMathSciNetCrossRefGoogle Scholar

A. Joye: Proof of the Landau—Zener formula, Asympt. Anal. 9 (1994), 209–258.MATHMathSciNetGoogle Scholar

A. Joye, Ch.-Ed. Pfister: Exponentially small adiabatic invariant for the Schrödinger equation, Commun. Math. Phys. 140 (1991), 15–41.MATHADSMathSciNetCrossRefGoogle Scholar

A. Joye, Ch.—Ed. Pfister: Superadiabatic evolution and adiabatic transition probability between two non—degenerate levels isolated in the spectrum, J. Math. Phys. 34 (1993), 454–479.MATHADSMathSciNetCrossRefGoogle Scholar

M. Kac: On distributions of certain Wiener functionals, Trans. Am. Math. Soc. 65 (1949), 1–13.MATHCrossRefGoogle Scholar

R.V. Kadison: Normal states and unitary equivalence of von Neumann alge bras, in the proceedings volume [[Kas]], pp. 1–18.Google Scholar

B. Karnarski: Generalized Dirac operators with several singularities, J. Oper ator Theory 13 (1985), 171–188.MATHMathSciNetGoogle Scholar

D. Kastler: The C*—algebra of a free boson field, I. Discussion of basic facts, Commun. Math. Phys. 1 (1965), 14–48.MATHADSMathSciNetCrossRefGoogle Scholar

T. Kato: Integration of the equations of evolution in a Banach space, J. Math. Soc. Jpn 5 (1953), 208–234.MATHCrossRefGoogle Scholar

T. Kato: Wave operators and similarity for some non—selfadjoint operators, Math. Ann. 162 (1966), 258–279.MATHMathSciNetCrossRefGoogle Scholar

T. Kato: Fundamental properties of Hamiltonian of the Schrödinger type, Trans. Am. Math. Soc. 70 (1951), 195–211.MATHCrossRefGoogle Scholar

T. Kato: On the existence of solutions of the helium wave equations, Trans. Am. Math. Soc. 70 (1951), 212–218.MATHCrossRefGoogle Scholar