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Kirsch W., Martinelli F.: On the spectrum of Schrödinger operators with a random potential; to appear in Comm. Math. Phys.
Kirsch W., Martinelli F.: On the ergodic properties of the spectrum of general random operators; to appear in Journal für die reine und angewandte Mathematik
Kirsch W., Martinelli F.: On the essential selfadjointness of stochastic Schrödinger operators; Preprint Bochum (1981)
Albeverio S., Høegh-Krohn R., Kirsch W., Martinelli F.: The spectrum of the three-dimensional Kronig-Penney' model with random point defects; to appear in Adv. in Applied Mathematics
Kirsch W.: über Spektren stochastischer Schrbdingeroperatoren; Thesis, Bochum (1981)
Reed M., Simon B.: Methods of modern Mathematical Physics Vol. II Academic Press, New York 1975
Pastur L.A.: Spectral properties of disordered systems in the one-body approximation; Comm. Math. Phys. 75, 179–196 (1980)
Kunz H., Souillard B.: Sur le spectre des opérateurs aux differences finies aléatoires; Comm. Math. Phys. 78, 201–246 (1980)
Simon B.: Almost Periodic Schrödinger operators: A Review; Adv. Appl. Math. to appear
Gol'dsheid I.J., Molchanov S.A., Pastur L.A.: A pure point spectrum of the stochastic one-dimensional Schrödinger operator; Funct. Anal. Appl. 11, 1–10 (1977)
Simon B.: Trace ideals and their applications, Cambridge University Press, 1979
Kallenberg O.: Random Measures, Akademie Verlag Berlin, 1976
Morgan J.D.: Schrödinger operators whose potentials have separated singularities; J. Oper. Theory 1, 109–115 (1979)
Reed M., Simon B.: Methods of Modern Mathematical Physics, Vol. I; Academic Press, New York 1972
Avron J., Simon B.: Almost periodic Schrödinger operators: I Limit periodic potentials; Comm. Math. Phys.
Moser J.: An example of a Schrödinger equations with almost periodic potential and nowhere dense spectrum; Preprint Zurich (1981)
Skriganov M.M.: Proof of the Bethe-Sommerfeld conjecture in dimension two; Soviet Math. Dokl. 20, 956–959 (1979)
Kronig R.L., Penney W.G.: Quantum mechanics of electrons in crystal lattices; Proc. Roy. Soc. (London) A130, 499–513; reprinted in [32]
Reed M., Simon B.: Methods of modern Mathematical Physics Vol. IV; Academic Press, New York 1978
Avron J., Grossmann A., Rodriguez R.: Spectral properties of reduced Bloch Hamiltonians; Ann. Phys. 103, 47–63 (1977)
Thomas L.E.: Time dependent approach to scattering from impurities in a crystal; Comm. Math:. Phys. 33, 335–343 (1973)
Saxom D.S., Hutner R.A.: Some electronic properties of a one-dimensional crystal model; Philips Res. Rep. 4, 81–122 (1949)
Flügge S.: Rechenmethoden der Quantenmechanik; Springer, Berlin 1975
Albeverio S., Høegh-Krohn R.: Point interaction as limit of short range interactions; J. Op. Theory 6, 313–339 (1981)
Albeverio S., Gesztesy F., Høegh-Krohn R.: The low energy expansion in non relativistic scattering theory; to appear in Ann. Inst. H. Poinc.
Albeverio S., Fenstad J.E., Høegh-Krohn R.: Singular perturbation and nonstandard analysis; Trans. Amer. Math. Soc. 252, 275–295 (1979)
Albeverio S., Fenatad J. E., Høegh-Krohn R., Lindstrøm T.: Nonstandard Analysis; book in preparation
Grossmann A., Høegh-Krohn R., Mebkhout M.: The one particle theory of point ihteractions; Comm. Math, Phys. 77, 87–110 (1480)
Luttinger J.M.; Wave propagation in one-dimensional structure; Philips Res. Rep. 6, 303–310 (1451) reprinted in [32]
Kerner E.H.: Periodic impurities. in a periodic lattice; Phys. Rev. 55, 687–689 (1454)
James H.M., Ginzharg A.S.: Band structure in disordered alloys and impurity semiconductors; J. Phys. Chem. 57, 840–848 (1453)
Lieb E.H., Mattis D.C.: Mathematical Physics in one dimension; Academic Press, New York 1966
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Kirsch, W., Martinelli, F. (1982). Some results on the spectra of random schrödinger operators and their application to random point interaction models in one and three dimensions. In: Albeverio, S., Combe, P., Sirugue-Collin, M. (eds) Stochastic Processes in Quantum Theory and Statistical Physics. Lecture Notes in Physics, vol 173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11956-6_122
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