@article{AIHPA_1995__62_4_361_0,
author = {Pankratova, T. F.},
title = {Semi-classical eigenstates at the bottom of a multidimensional well},
journal = {Annales de l'I.H.P. Physique th\'eorique},
volume = {63},
year = {1995},
pages = {361-382},
mrnumber = {1343782},
zbl = {0835.35120},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPA_1995__62_4_361_0}
}
Pankratova, T. F. Semi-classical eigenstates at the bottom of a multidimensional well. Annales de l'I.H.P. Physique théorique, Tome 63 (1995) pp. 361-382. http://gdmltest.u-ga.fr/item/AIHPA_1995__62_4_361_0/
[1] , Asymptotics of the Point Spectrum of the Operator W'' + λ2p(x) W, Mat. Sb., Vol. 68, (110), 1965, pp. 81-110 (Russian).
[2] , Asymptotics of Singular Sturm-Liuville Problems with Respect to a Large Parameter in the Case of Close Transition Points, Differentsial'nye Uravneniya, Vol. 5, 1969, pp. 313-325, English transl. in Differential Equations, Vol. 5, 1969. | MR 245921 | Zbl 0249.34012
[3] , The Spectrum Splitting Generated by a Potential Barrier in Problems with a Symmetrical Potential, Differentsial'nye Uravneniya, Vol. 18, 1982, pp. 1971-1975, English transl. in Differential Equations, Vol. 18, 1982. | MR 681980 | Zbl 0522.34020
[4] , Semiclassical Analysis of Low Lying Eigenvalues, I. Non-Degenerate Minima: Asymptotic Expansions, Ann. Inst. Henry Poincaré, Vol. 38, 1983, pp. 295-307. | Numdam | MR 708966 | Zbl 0526.35027
[5] , Semiclassical Analysis of Low Lying Eigenvalues, II. Tunneling, Ann. Math., Vol. 120, 1984, pp. 89-118. | MR 750717 | Zbl 0626.35070
[6] , The Complex WKB-Method in Nonlinear Equations, Nauka, Moscow, 1981 (Russian).
[7] , and , New Approach to the Semiclassical Limit of Quantum Mechanics, Comm. Math. Phys., Vol. 80, 1981, pp. 223-254. | MR 623159 | Zbl 0483.60094
[8] , Double Wells, Comm. Math. Phys., Vol. 75, 1980, pp. 239-261. | MR 581948 | Zbl 0445.35036
[9] , Quasimodes and Splitting of Eigenvalues, Soviet Math. Dokl., Vol. 29, 1984, pp. 597-601. | MR 754093 | Zbl 0592.34012
[10] and , Contribution à la resurgence quantique, Thèse de doctorat de Math., Université de Nice-Sophia-Antipolis.
[11] and , Multiple Wells in the Semi-Classical Limit I, Comm. in Partial Differential Equations, Vol. 9, 1984, pp. 337-408. | MR 740094 | Zbl 0546.35053
[12] and , Puits Multiples en Limite Semi-Classical II. Interaction moléculaire. Symétries. Perturbation, Ann. Inst. Henry Poincaré, Vol. 42, 1985, pp. 127- 212. | Numdam | MR 798695 | Zbl 0595.35031
[13] and , Multiple Wells in the Semi-Classical Limit III. Interaction Through Non-Resonant Wells, Math. Nachr., Vol. 124, 1985, pp. 263-313. | Zbl 0597.35023
[14] , and , Multiple Tunneling in d-Dimensions: a Quantum Particle in a Hierarchical Potential, Ann. Inst. Henry Poincaré, Vol. 42, 1985, pp. 73-108. | Numdam | MR 794366 | Zbl 0586.35030
[15] and , The Quantization of Lower States of an Unharmonic Oscillator with Methods of the Classical Dynamics., Problemy Matfiziki, vyp 13, 1991 (Russian).
[16] and , The Schrödinger Equation and Canonical Perturbation Theory, Comm. Math. Phys., Vol. 108, 1987, pp. 25-40. | MR 872139 | Zbl 0622.35071
[17] and , Heisenberg's Picture and Noncommutative Geometry of the Semiclassical Limit in Quantum Mechanics, Ann. Inst. Henry Poincaré, Vol. 52, 1990, pp. 175-235. | Numdam | MR 1057445 | Zbl 0705.46037
[18] , and , The Splitting of the Low Lying Energy Levels of the Schrödinger Operator and the Asymptotics of the Fundamental Solution of the Equation hut = (h2Δ/2 - V (x))u with a Symmetric Potential, Teoret. Mat. Fiz., Vol. 87, 1991, pp. 323-375, English transl. in Theoret. and Math. Phys., Vol. 87, 1991. | MR 1129671 | Zbl 0745.35033
[19] , and , Quantization of the Bellman Equation. Exponential Asymptotics and Tunneling, Advances in Soviet Mathematics, Vol. 13, 1992, pp. 1-46. | MR 1203783 | Zbl 0796.35141
[20] and , Splitting Amplitudes of the Lowest Energy Levels of the Schrödinger Operator with Double well Potential, Teoret. Mat. Fiz., Vol. 94, 1993, pp. 346-434, English transl. in Theoret. and Math. Phys., Vol. 94, 1993. | MR 1226223 | Zbl 0799.35050
[21] , Modes and Quasi-Modes, Functional. Anal. i. Prilozhen, Vol. 6, 1972, pp. 12-20, English transl. in Functional Anal. Appl., Vol. 6, 1972 (Russian). | Zbl 0251.70012
[22] , Mathematical Methods in Classical Mechanics, Nauka, Moscow, 1989, (Russian). | MR 1037020 | Zbl 0692.70003
[23] , and , Dynamical Systems-3. Mathematical Aspects in Classical and Celestial Mechanics, Itogi Nauki i Tekhnik. Modern Problems in Mathematics. Fundamental Orientations, Viniti ANSSSR Eds., Vol. 3, Moscow, 1985 (Russian). | Zbl 0674.70003
[24] , On the Algebraic Problem Concerning the Normal Forms of Linear Dynamical Systems, Amer. J. Math., Vol. 58, 1936, pp. 141-163. | JFM 62.1795.10 | MR 1507138 | Zbl 0013.28401
[25] , The Exponential Representation of Canonical Matrices, Amer. J. Math., Vol. 61, 1939, pp. 897-911. | MR 220 | Zbl 0022.10007
[26] , Analytic Wavefront Sets and Operators with Multiple Characteristics, Hokkaido Math. J., Vol. 12, 1983, pp. 392-433. | MR 725588 | Zbl 0531.35022
[27] and , Germes de configurations legendriennes stables et functions d'Airy-Weber generalisees, Annales de l'Institut Fourier, Grenoble, Vol. 41, 1991, pp. 905-936. | Numdam | MR 1150572 | Zbl 0741.58048
[28] and , Functional Analysis, Nauka, 2nd rev., Moscow, 1977, English transl., Pergamon Press, 1982. | MR 664597 | Zbl 0484.46003