@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://archive.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://archive.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://archive.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://archive.numdam.org/item/AIHPA_1991__55_1_459_0/
[ADH] 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
, et ,[A] Lectures on Exponential Decay of Solutions of Second Order Elliptic Equation, Princeton University Press, 1982. | MR | Zbl
,[B] Scattering from Impurities in a Crystal., Comm. Math. Phys., vol. 46, 1976, p. 153-166. | MR
,[Bi] Perturbations of Operators with Periodic Coefficients, Proceedings of the conference Schrödinger Operators: Standard and non-standard, Dubna, 1988.
,[C] Energy Band Theory, Academic Press, New York/London, 1964. | MR | Zbl
,[Ca] An Infinite Number of Wells in the Semi-Classical limit, Preprint de l'université de Lund, 1989, Asympt. Anal. (à paraître). | MR
,[DH] 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] Trapping and Cascading of Eigenvalues in the Large Coupling Limit., Com. Math. Phys., vol. 118, 1988, p. 597-634. | MR | Zbl
, , , , , et ,[GS] On a Theorem of Deift and Hempel., Comm. Math. Phys., vol. 116, 1988, p. 503-505. | MR | Zbl
, ,[HSj1] Multiple Wells in the Semi-Classical Limit 1, Comm. P.D.E., vol. 9, (4), 1984, p. 337-408. | MR | Zbl
, et ,[HSj2] 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] Effet tunnel pour l'opérateur de Schrödinger semiclassique I., Actes des Journées des E.D.P., Saint-Jean-de-Monts, 1985. | Zbl
et ,[K] Some Applications of the Birman-Schwinger Principle., Helv. Phys. Acta, vol. 55, 1982, p. 49-68. | MR
,[KS] Coupling Constant Thresholds in Non Relativistic Quantum Mechanics., Ann. Phys., vol. 130, 1980, p. 251-281. | MR | Zbl
et ,[LL] Mécanique quantique, théorie non relativiste, Editions MIR, Moscou, 1966. | Zbl
et ,[O] Comportement semi-classique pour l'opérateur de Schrödinger à potentiel périodique, J. Funct. Anal., vol. 72, 1987, p. 65-93. | MR | Zbl
,[P] 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] On the Absorption of Eigenvalues by Continuous Spectra in Regular Perturbation Problems., J. Funct. Anal., vol. 25, 1977, p. 338-344. | MR | Zbl
,[S2] 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] Semi-Classical Analysis of Low Lying Eigenvalues II. Tunneling., Ann. Math., vol. 120, 1984, p. 89-118. | MR | Zbl
,[S4] 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] 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] 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] Geometric and Arithmetic Methods in the Spectral Theory of Multidimensional Periodic Operators., Proc. the Steklov Inst. Math., vol. 2, 1987. | MR | Zbl
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