Scattering theory in quantum mechanics and asymptotic completeness

  • J. M. Combes
Main Lectures
Part of the Lecture Notes in Physics book series (LNP, volume 80)


Scattering Theory Faddeev Equation Singular Potential Kinetic Energy Operator Scatter Theory 


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  1. [1]
    T. KATO Perturbation Theory for Linear Operators Springer, New York (1966).Google Scholar
  2. [2]
    S.T. KURODA Scattering Theory for Differential Operators II. J.Math.Soc.Japan 25, 643 (1973).Google Scholar
  3. [3]
    H. EKSTEIN Theory of Time-Dependent Scattering Multichannel Processes Phys. Rev. 101, 880 (1956).CrossRefGoogle Scholar
  4. [4]
    B. SIMON, M. REED Methods of Modern Mathematical Physics II. Fourier Analysis, Self-Adjointness Acad. Press (1975).Google Scholar
  5. [5]
    D.W. ROBINSON Scattering Theory with Singular Potentials Ann. I.H.P. 21 (1974).Google Scholar
  6. [6]
    P. FERRERO, O. de PAZZIS, D.W. ROBINSON Ann. I.H.P., 21, 217 (1974).Google Scholar
  7. [7]
    J. HOWLAND Banach Space Techniques in Perturbation Theory of Self-Adjoint Operators with Continuous Spectra J. Math. Anal. and Appl., 20, 22 (1967).Google Scholar
  8. [8]
    S. AGMON Ann. Scuol. Norm. Sup. Pisa, Ser. IV, 2, 151.Google Scholar
  9. [9]
    J.L. LIONS, E. MAGENES Problèmes aux limites non homogènes et applications Dunod, Paris (1968).Google Scholar
  10. [10]
    T. KATO Wave-Operators and Similarity for Some Non Self-Adjoint Operators Math. Ann. 162, 258 (1966).Google Scholar
  11. [11]
    T. KATO Smooth Operators and Commutators Studia Math. T. XXXI, 535 (1968).Google Scholar
  12. [12]
    T. KAKO, K. YAJIMA Spectral and Scattering Theory for a Class of Non Self-Adjoint Operators Scient. Pap. of the College of Gen. Educ., Tokyo 26, 73 (1976).Google Scholar
  13. [13]
    R. LAVINE Commutators and Scattering Theory II Ind. Univ. Math. 21, 643 (1973).Google Scholar
  14. [14]
    M. SCHECTER Scattering Theory for Elliptic Operators of Arbitrary Order Com.Math. Helv. 49, 84 (1974).Google Scholar
  15. [15]
    PINCHUK Thesis, Univ. of California, Berkeley (1975).Google Scholar
  16. [16]
    KITADA To appear.Google Scholar
  17. [17]
    J.D. DOLLARD Asymptotic Convergence and the Coulomb Interaction J. Math. Phys. 5, 729 (1964).Google Scholar
  18. [18]
    V.S. BULSLAEV and V.B. MATVEEV Wave-Operators for the Schrödinger Equation with Slowly Decreasing Potential Teoret. Mat. Fiz. 1, 367 (1970).Google Scholar
  19. [19]
    H. EKSTEIN Scattering in Field Theory Nuovo Cimento 4, 1017 (1956).Google Scholar
  20. [20]
    E. MOURRE Application de la méthode de Lavine au problème à trois corps Ann. I.H.P. vol. XXVI, 3 (1977).Google Scholar
  21. [21]
    IORIO, O' CARROL Asymptotic Completeness for Multi-Particle Schrödinger Hamiltonians with Weak Potentials Commun.math. Phys. 27, 137 (1972).Google Scholar
  22. [22]
    L.D. FADDEEV Mathematical Aspects of the Three Body Problem in the Quantum Theory of Scattering Israel Scientific Translation (1965).Google Scholar
  23. [23]
    O.A. YAKUBOVSKY On the Integral Equations in the Theory of N-Particle Systems J. Nucl. Phys. (USSR) 5, 1312 (1967).Google Scholar
  24. [24]
    R. NEWTON J. Math. Phys. 12, 1552 (1971).Google Scholar
  25. [25]
    M. COMBESCURE, J. GINIBRE Ann. Phys. 101 (1976).Google Scholar
  26. [26]
    L.E. THOMAS Asymptotic Completeness in 2 and 3 Particle Quantum Mechanical Systems Ann. Phys. 90, 127 (1975).Google Scholar
  27. [27]
    K.M. WATSON Phys. Rev. 89, 575 (1953).Google Scholar
  28. [28]
    K. YAJIMA An Abstract Stationary Approach to 3-Body Scattering To appear (presented at Oberwolfach Conference, July 1977).Google Scholar
  29. [29]
    K. HEPP On the Quantum Mechanical N-Body Problem Helv. Phys. Acta 42, 425 (1969).Google Scholar
  30. [30]
    W. THIRRING, P. URBAN The Schrödinger Equation Springer-Verlag (1977).Google Scholar
  31. [31]
    I. SIGAL Preprint E.T.H. (1977).Google Scholar
  32. [32]
    J.M. COMBES in Scattering Theory in Mathematical Physics J.A. Lavita and J.P. Marchand Ed., Reidel, Dortrecht (1974).Google Scholar
  33. [33]
    W. HUNZIKER Helv. Phys. Acta 39, 451 (1966).Google Scholar
  34. [34]
    E. BALSLEV, J.M. COMBES Spectral Properties of Schrödinger Hamiltonians with Dilation Analytic Potentials Commun.math. Phys. 22, 280 (1971).Google Scholar
  35. [35]
    A. TIP A Note on the Analyticity of the Elastic Forward Electron-Atom Exchange Scattering Amplitude Preprint FOM Institut voor Atom, Amsterdam (1977).Google Scholar
  36. [36]
    R.T. PROSSER Convergent Perturbation Expansions for Certain Wave-Operators J.M.P. 5, 708 (1964).Google Scholar
  37. [37]
    J.M. COOK Convergence of the Möller Wave-Matrix J.M.P. 36, 82 (1957).Google Scholar
  38. [38]
    M. SCHECTER A New Criterion for Scattering Theory Yeshiva Preprint (1977).Google Scholar
  39. [39]
    B. SIMON Scattering Theory and Quadratic Forms: on a Theorem of Schecter Yeshiva Preprint (1977).Google Scholar
  40. [40]
    J. HOWLAND Abstract Stationary Theory of Multichannel Scattering J. Funct. Anal. 22, 250 (1976).Google Scholar
  41. [41]
    G.A. HAGEDORN Asymptotic Completeness for a Class of Four Particle Schrödinger Operators, Preprint Univ. Princeton.Google Scholar
  42. [42]
    P. ALSHOM, T. KATO Scattering by Long-Range Potentials Proceed. Symp. in Pure Math. 23, AMS, 393 (1973).Google Scholar
  43. [43]
    L. HORMANDER The Existence of Wave-Operators in Scattering Theory Math. Z. 146, 69 (1976).Google Scholar
  44. [44]
    A. BERTHIER, P. COLLET Wave-Operators for Momentum Dependent Long-Range Potentials Preprint Univ. Paris VI.Google Scholar
  45. [45]
    P. LAX, R. PHILLIPS Scattering Theory. Academic Press, New York, 1967.Google Scholar
  46. [46]
    J.D. DOLLARD Scattering into Cones Commun.math.Phys. 12, 193 (1968) and J. Math. Phys. 14, 708 (1973).Google Scholar
  47. [47]
    J.M. COMBES, R. NEWTON, R. STOKHAMER Scattering into Cones and Flux across Surfaces Phys. Rev. D, 11, 366 (1975).Google Scholar
  48. [48]
    H. EKSTEIN Scattering without Scattering Operators Annals of Physics 74, 303 (1972).Google Scholar
  49. [49]
    W. HUNZIKER in Scattering Theory in Mathematical Physics Reidel, 1974.Google Scholar
  50. [50]
    B. SIMON Wave-Operators for Classical Particle Scattering Commun.math.Phys. 23, 37 (1971).Google Scholar
  51. [51]
    S. ALBEVERIO, R. HOEGH-KROHN Proceedings of this Conference.Google Scholar
  52. [52]
    V.P. MASLOV The Quasi-Classical Asymptotic Solutions of some Problems in Mathematical Physics Zh. Vychisl. Mat. 1, 113 (1961).Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • J. M. Combes
    • 1
    • 2
  1. 1.Département de MathématiquesCentre Universitaire de ToulonFrance
  2. 2.Centre de Physique Théorique, CNRSMarseille

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