Eigenvalue asymptotics related to impurities in crystals
Méthodes semi-classiques Volume 2 - Colloque international (Nantes, juin 1991), Astérisque, no. 210 (1992), pp. 183-196.
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Hempel, Rainer. Eigenvalue asymptotics related to impurities in crystals, in Méthodes semi-classiques Volume 2 - Colloque international (Nantes, juin 1991), Astérisque, no. 210 (1992), pp. 183-196. http://archive.numdam.org/item/AST_1992__210__183_0/

[1] S. Alama, P. A. Deift and R. Hempel : Eigenvalue branches of the Schrödinger operator H-λW in a spectral gap of H . Commun. Math. Phys. 121 (1989), 291-321.

[2] S. Alama and Y. Y. Li: Existence of solutions for semilinear elliptic equations with indefinite linear part. Preprint, 1990.

[3] N. W. Ashcroft and N. D. Mermin: Solid State Physics. Holt, Rinehart and Winston, New York 1976.

[4] M. Sh. Birman: Discrete spectrum in the gaps of the continuous one in the large coupling constant limit. In : Operator Theory : Advance and Applications, Vol. 46. Birkhäuser, Basel 1990.

[5] Ph. Briet, J. M. Combes and P. Duclos: Spectral stability under tunneling. Commun. Math. Phys. 126 (1989), 133-156.

[6] R. Courant and D. Hilbert: Methods of Mathematical Physics. Vol. I. Interscience, New York 1953.

[7] P. A. Deift and R. Hempel: On the existence of eigenvalues of the Schrödinger operator H-λW in a gap of σ(H). Commun. Math. Phys. 103 (1986), 461-490.

[8] P. A. Deift and B. Simon: On the decoupling of finite singularities from the question of asymptotic completeness in two-body quantum systems. J. Funct. Anal. 23 (1976), 218-238.

[9] M. S. P. Eastham: The spectral theory of periodic differential equations. Scottish Academic Press, Edinburgh 1973.

[10] F. Gesztesy, D. Gurarie, H. Holden, M. Klaus, L. Sadun, B. Simon and P. Vogl: Trapping and cascading of eigenvalues in the large coupling limit. Commun. Math. Phys. 116 (1988), 597-634.

[11] F. Gesztesy and B. Simon: On a theorem of Deift and Hempel. Commun. Math. Phys. 116 (1988), 503-505.

[12] I. C. Gohberg and M. G. Krein: Introduction to the Theory of Linear Non-selfadjoint Operators. Amer. Math. Soc., Providence (R. I.) 1969.

[13] R. Hempel: A left-indefinite generalized eigenvalue problem for Schrödinger operators. Habilitations schrift, Univ. München 1987.

[14] R. Hempel: On the asymptotic distribution of the eigenvalue branches of the Schrödinger operator H+λW in a spectral gap of H. J. Reine Angew. Math. 399 (1989), 38-59.

[15] R. Hempel: Eigenvalues in gaps and decoupling by Neumann boundary conditions. J. Math. Anal. Appl., to appear.

[16] T. Kato: Perturbation theory for linear operators. Springer, New York 1966.

[17] W. Kirsch: Small perturbations and the eigenvalues of the Laplacian on large bounded domains. Proc. Amer. Math. Soc. 101 (1987), 509-512.

[18] M. Klaus: Some applications of the Birman-Schwinger principle. Helv. Phys. Acta 55 (1982), 49-68.

[19] F. Klopp: Impuretés dans une structure périodique. Journées " Équations aux dérivées partielles " (Saint Jean des Monts, 1990), Exp. No. XX, Ecole Polytech., Palaiseau, 1990

[20] A. Outassourt: Comportement semi-classique pour l'opérateur de Schrödinger à potentiel périodique. J. Funct. Anal. 72 (1987), 65-93.

[21] S. T. Pantelides: The electronic structure of impurities and other point defects in semiconductors. Rev. Mod. Phys. 50 (1978), 797-858.

[22] M. Reed and B. Simon: Methods of modern mathematical physics. Vol. I. Functional Analysis. Revised and enlarged ed. Academic Press, New York 1981.

[23] M. Reed and B. Simon: Methods of modern mathematical physics. Vol. III. Scattering theory. Academic Press, New York 1979.

[24] M. Reed and B. Simon: Methods of modern mathematical physics. Vol. IV. Analysis of operators. Academic Press, New York 1978.

[25] B. Simon: Trace Ideals and their applications. Cambridge Univ. Press, London 1979.

[26] B. Simon: A canonical decomposition for quadratic forms with application to monotone convergence theorems. J. Funct. Anal. 28 (1978), 377-385.

[27] J. Weidmann: Stetige Abhängigkeit der Eigenwerte und Eigenfunktionen elliptischer Differentialoperatoren vom Gebiet. Math. Scand. 54 (1984), 51- 69.

[28] A. V. Sobolev: The Weyl asymptotics for discrete spectrum of the perturbed Hill operator. Preprint, 1991