Étude semi-classique d'une perturbation d'un opérateur de Schrödinger périodique
Annales de l'I.H.P. Physique théorique, Tome 55 (1991) no. 1, pp. 459-509.
@article{AIHPA_1991__55_1_459_0,
     author = {Klopp, Fr\'ed\'eric},
     title = {\'Etude semi-classique d'une perturbation d'un op\'erateur de {Schr\"odinger} p\'eriodique},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {459--509},
     publisher = {Gauthier-Villars},
     volume = {55},
     number = {1},
     year = {1991},
     mrnumber = {1130214},
     zbl = {0754.35100},
     language = {fr},
     url = {http://www.numdam.org/item/AIHPA_1991__55_1_459_0/}
}
TY  - JOUR
AU  - Klopp, Frédéric
TI  - Étude semi-classique d'une perturbation d'un opérateur de Schrödinger périodique
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1991
SP  - 459
EP  - 509
VL  - 55
IS  - 1
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1991__55_1_459_0/
LA  - fr
ID  - AIHPA_1991__55_1_459_0
ER  - 
%0 Journal Article
%A Klopp, Frédéric
%T Étude semi-classique d'une perturbation d'un opérateur de Schrödinger périodique
%J Annales de l'I.H.P. Physique théorique
%D 1991
%P 459-509
%V 55
%N 1
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPA_1991__55_1_459_0/
%G fr
%F AIHPA_1991__55_1_459_0
Klopp, Frédéric. Étude semi-classique d'une perturbation d'un opérateur de Schrödinger périodique. Annales de l'I.H.P. Physique théorique, Tome 55 (1991) no. 1, pp. 459-509. http://www.numdam.org/item/AIHPA_1991__55_1_459_0/

[ADH] S. Alama, P. Deift et R. Hempel, Eigenvalue Branches of the Schrôdinger Operator H-λ W in a Gap of σ(H), Comm. Math. Phys., vol. 121, 1989, p. 291- 321. | MR | Zbl

[A] S. Agmon, Lectures on Exponential Decay of Solutions of Second Order Elliptic Equation, Princeton University Press, 1982. | MR | Zbl

[B] F. Bentosela, Scattering from Impurities in a Crystal., Comm. Math. Phys., vol. 46, 1976, p. 153-166. | MR

[Bi] M.Sh. Birman, Perturbations of Operators with Periodic Coefficients, Proceedings of the conference Schrödinger Operators: Standard and non-standard, Dubna, 1988.

[C] J. Callaway, Energy Band Theory, Academic Press, New York/London, 1964. | MR | Zbl

[Ca] U. Carlsson, An Infinite Number of Wells in the Semi-Classical limit, Preprint de l'université de Lund, 1989, Asympt. Anal. (à paraître). | MR

[DH] P. Deift, R. Hempel, On the Existence of Eigenvalues of the Schrödinger Operator H-λ W in a Gap of σ(H), Comm. Math. Phys., vol. 103, 1986, p. 461- 490. | MR | Zbl

[GHKSV] F. Gesztesy, D. Gurarie, H. Holden, M. Klaus, L. Sadun, B. Simon et P. Vogl, Trapping and Cascading of Eigenvalues in the Large Coupling Limit., Com. Math. Phys., vol. 118, 1988, p. 597-634. | MR | Zbl

[GS] F. Gesztesy, B. Simon, On a Theorem of Deift and Hempel., Comm. Math. Phys., vol. 116, 1988, p. 503-505. | MR | Zbl

[HSj1] B. Helffer, et J. Sjöstrand, Multiple Wells in the Semi-Classical Limit 1, Comm. P.D.E., vol. 9, (4), 1984, p. 337-408. | MR | Zbl

[HSj2] B. Helffer, J. Sjöstrand, Puits multiples en limite semi-classique 2. Interaction moléculaire. Perturbations, Annales Inst. Henri Poincaré, Phys. Théor., vol. 42, (2), 1985, p.127-212. | Numdam | MR | Zbl

[HSj3] B. Helffer et J. Sjöstrand, Effet tunnel pour l'opérateur de Schrödinger semiclassique I., Actes des Journées des E.D.P., Saint-Jean-de-Monts, 1985. | Zbl

[K] M. Klaus, Some Applications of the Birman-Schwinger Principle., Helv. Phys. Acta, vol. 55, 1982, p. 49-68. | MR

[KS] M. Klaus et B. Simon, Coupling Constant Thresholds in Non Relativistic Quantum Mechanics., Ann. Phys., vol. 130, 1980, p. 251-281. | MR | Zbl

[LL] L. Landau et E. Lifschitz, Mécanique quantique, théorie non relativiste, Editions MIR, Moscou, 1966. | Zbl

[O] A. Outassourt, Comportement semi-classique pour l'opérateur de Schrödinger à potentiel périodique, J. Funct. Anal., vol. 72, 1987, p. 65-93. | MR | Zbl

[P] A. Persson, Bounds for the Discrete Part of the Spectrum of a Semi-Bounded Schrôdinger Operator, Math. Scand., vol. 8, 1960, p. 143-153. | MR | Zbl

[S1] B. Simon, On the Absorption of Eigenvalues by Continuous Spectra in Regular Perturbation Problems., J. Funct. Anal., vol. 25, 1977, p. 338-344. | MR | Zbl

[S2] B. Simon, Semi-Classical Analysis of Low Eigenvalues I. Nondegenerate Minima: Asymptotic Expansion., Annales Inst. Henri Poincaré, Phys. Théor., vol. 38, (3), 1983, p. 295-307. | Numdam | MR | Zbl

[S3] B. Simon, Semi-Classical Analysis of Low Lying Eigenvalues II. Tunneling., Ann. Math., vol. 120, 1984, p. 89-118. | MR | Zbl

[S4] B. Simon, Semi-Classical Analysis of Low Lying Eigenvalues III. Width of the Ground State Band in Strongly Coupled Solids., Ann. Phys., vol. 158, (2), 1984, p. 415-420. | MR | Zbl

[S5] B. Simon, The Bound State of a Weakly Coupled Schrôdinger Operator in One or Two Dimensions., Ann. Phys., vol. 97, 1976, p. 279-288. | MR | Zbl

[Sj] J. Sjöstrand, Microlocal Analysis for the Periodic Magnetic Schrôdinger Equation and Related Questions, C.I.M.E. Lectures, Été 1989, L.N.M. Springer (à paraître). | MR

[Sk] M.M. Skriganov, Geometric and Arithmetic Methods in the Spectral Theory of Multidimensional Periodic Operators., Proc. the Steklov Inst. Math., vol. 2, 1987. | MR | Zbl