Asymptotic -expansions of stationary quantum states
Annales de l'I.H.P. Physique théorique (1977)
- Volume: 26, Issue: 4, page 343-403
- ISSN: 0246-0211
Access Full Article
topHow to cite
topVoros, A.. "Asymptotic $\hbar $-expansions of stationary quantum states." Annales de l'I.H.P. Physique théorique 26.4 (1977): 343-403. <http://eudml.org/doc/75944>.
@article{Voros1977,
author = {Voros, A.},
journal = {Annales de l'I.H.P. Physique théorique},
language = {eng},
number = {4},
pages = {343-403},
publisher = {Gauthier-Villars},
title = {Asymptotic $\hbar $-expansions of stationary quantum states},
url = {http://eudml.org/doc/75944},
volume = {26},
year = {1977},
}
TY - JOUR
AU - Voros, A.
TI - Asymptotic $\hbar $-expansions of stationary quantum states
JO - Annales de l'I.H.P. Physique théorique
PY - 1977
PB - Gauthier-Villars
VL - 26
IS - 4
SP - 343
EP - 403
LA - eng
UR - http://eudml.org/doc/75944
ER -
References
top- [1] A. Messiah, Mécanique Quantique. Dunod, Paris, 1965. MR129304
- [2] L. Landau- E. Lifschitz, Mécanique Quantique, Mir (Moscow).
- [3] J.B. Keller, Ann. Phys., t. 4, 1958, p. 180. Zbl0085.43103MR99207
- [4] V.P. Maslov, Théorie des Perturbations. Dunod, Paris, 1972 (translated by J. LASCOUX and R. SÉNÉOR, includes refs. [45] [46]).
- [5] R. Courant, D. Hilbert, Methods of Mathematical Physics II. Interscience, 1962. Zbl0099.29504
- [6] D. Ludwig, Comm. Pure Appl. Math., t. 13, 1960, p. 473. Zbl0098.29601MR115010
- [7] L. Hörmander, Acta Math., t. 127, 1971, p. 79; L. Hormander, J.J. Duistermaat, Acta Math., t. 128, 1972, p. 183. Zbl0232.47055MR388463
- [8] J.J. Duistermaat, Fourier Integral Operators. Courant Institute Press, 1973. Zbl0272.47028MR451313
- [9] J. Chazarain (Ed.), Fourier Integral Operators and Partial Differential Equations (Proc. 1974, Conference, Nice). SpringerLecture Notes in Mathematics, vol. 459, 1975. Zbl0299.00021MR388171
- [10] H. Komatsu ( Ed.), Hyperfunctions and Pseudo-differential Equations. SpringerLecture Notes in Mathematics, vol. 287, 1973 ; F. Pham (Ed.), Hyperfunctions and Zbl0253.00006MR388082
- Theoretical Physics. Springer Lectures Notes in Mathematics, vol. 449, 1975 ; J. Bros, D. Iagolnitzer, Ann. Inst. H. Poincaré, t. 18, 1973, p. 147 and Séminaire Goulaouic-Lions-Schwartz, Lecture n° 18, 1975.
- [11] Colloque International C. N. R. S., n° 237: Géométrie Symplectique et Physique Mathématique (Proc. 1974 Conference, Aix-en-Provence), C. N. R. S., Paris, 1975. MR424458
- [12] J.J. Duistermaat, Comm. Pure Appl. Math., t. 27, 1974, p. 207. Zbl0285.35010MR405513
- [13] V. Guillemin, S. Sternberg, Geometric Asymptotics. A. M. S., to appear. Zbl0364.53011
- [14] E. Wigner, Phys. Rev., t. 40, 1932, p. 749; J.C.T. Pool, J. Math. Phys., t. 7, 1966, p. 66; K. Imre et al., J. Math. Phys., t. 8, 1967, p. 1097.
- [15] A. Grossmann, G. Loupias, E.M. Stein, Ann. Inst. Fourier, t. 18, 1969, p. 343. Zbl0176.45102MR267425
- [16] H.J. Groenewold, Physica, t. 12, 1946, p. 405 ; J.E. Moyal, Proc. Cambridge Phil. Soc., t. 45, 1949, p. 99; R. Hermann, The Poisson-Moyal Bracket. Harvard University, Physics Dept. preprint, 1976. MR18562
- [17] D. Kastler, Comm. Math. Phys., t. 1, 1965, p. 14 ; G. Loupias, S. Miracle-Sole, Comm. Math. Phys., t. 2, 1966, p. 31. Zbl0137.45601MR193983
- [18] N. March, J. Plaskett, Proc. Roy. Soc., t. A 235, 1956, p. 419. Zbl0071.22601MR78500
- [19] G. Baraff, S. Borowitz, Phys. Rev., t. 121, 1961, p. 1704 ; R. Balian, C. Bloch, Ann. Phys., t. 63, 1971, p. 592. MR118376
- [20] R. Feynman, A. Hibbs, Quantum Mechanics and Path. Integrals. McGraw Hill, 1965; C. De Witt, Comm. Math. Phys., t. 28, 1972, p. 47 and t. 37, 1974, p. 63. Zbl0287.28006
- [21] R. Balian, C. Bloch, Ann. Phys., t. 60, 1970, p. 401 ; t. 64, 1971, p. 271 ; t. 69, 1972, p. 76. Zbl0207.40202
- [22] M. Berry, K. Mount, Rep. Prog. Phys., t. 35, 1972, p. 315.
- [23] J. Leray, in [9] [11].
- [24] J.M. Souriau, Comm. Math. Phys., t. 1, 1966, p. 374 and Structure des Systèmes Dynamiques. Dunod, Paris, 1970. MR207332
- [25] B. Kostant, in Springer Lecture Notes in Mathematics, vol. 170, 1970. MR294568
- [26] K. Maurin, R. Raczka, Mathematical Physics and Physical Mathematics. Proc., 1974, Conference, Warsaw, Reidel, 1976. Zbl0327.00001MR550910
- [27] A. Voros, Ann. Inst. H. Poincaré, t. 24, 1976, p. 31. MR420747
- [28] Y. Colin De Verdière, Compositio Math., t. 27, 1973, p. 159. Zbl0281.53036MR348798
- [29] Y. Colin De Verdière, Quasi-Modes sur les Variétés Riemanniennes. Preprint, Paris VII University. MR501196
- [30] J.J. Duistermaat, V. Guillemin, Inventiones Math., t. 29, 1975, p. 39. Zbl0307.35071MR405514
- [31] M. Gutzwiller, J. Math. Phys., t. 12, 1971, p. 343 ; A. Voros, in [11]; R. Dashen, B. Hasslacher, A. Neveu, Phys. Rev., t. D 10, 1974, p. 4114 and t. D 11, 1975, p. 3424.
- [32] V. Guillemin, in [11].
- [33] B. Kostant, Symposia Math., t. 14, 1974, p. 139; R. Blattner, B. Kostant, S. Stern- BERG, in [11].
- [34] L. Van Hove, Acad. Roy. Belg. Bull. Class. Sci., t. 37, 1951, p. 610. Zbl0044.23103MR45059
- [35] I. Segal, Mat. Fys. Medd. Danske Vid. Selk., t. 31, 1959, p. 1; D. Shale, Trans. A. M. S., t. 103, 1962, p. 149; A. Weil, Acta Math., t. 111, 1963, p. 143. MR112626
- [36] L. Landau, E. Lifschitz, Mécanique, Mir. Moscow.
- [37] R. Abraham, J. Marsden, Foundations of Mechanics. Benjamin, 1967. Zbl0158.42901
- [38] G. Mackey, Mathematical Foundations of Quantum Mechanics. Benjamin, 1967.
- [39] L. Schwartz, Théorie des Distributions. Hermann, 1957. Zbl0078.11003MR209834
- [40] B. Simon, M. Reed, Methods of Modern Mathematical Physics. Academic Press, 1972 and 1975. MR493419
- [41] H. Weyl, H. Robertson, Theory of Groups and Quantum Mechanics. Dover. Zbl55.0247.02
- [42] V.V. Grushin, Funct. Anal. and Appl. (Russian), t. 4 (3), 1970, p. 37; L. Boutet De Monvel, Comm. Pure Appl. Math., t. 27, 1974, p. 585. Zbl0223.35084
- [43] C. Rockland, Hypoellipticity and Eigenvalue Asymptotics. Lecture Notes in Mathematics.Springer, 1975, p. 464. Zbl0302.35002MR501202
- [44] H. Araki, Private communication.
- [45] V. Arnold, Funct. Anal. and Appl. (russe), t. 1, 1967, p. 1 ; translated in [4].
- [46] V. Bouslaiev, Funct. Anal. and Appl. (russe), t. 3, 1969, p. 17; translated in [4].
- [47] M. Moshinsky, C. Quesne, J. Math. Phys., t. 12, 1971, p. 1772. Zbl0247.20051MR286385
- [48] G. Mackey, Induced Representations of Groups and Quantum Mechanics. Benjamin, 1968. Zbl0174.28101MR507212
- [49] J.M. Souriau, In 4th Colloquium on Group Theoretical Methods in Physics. Univ. Nijmegen, 1975.
- [50] I.M. Gelfand, N. Vilenkin, Generalized Functions IV. Academic Press, 1964.
- [51] K. Nomizu, Lie Groups and Differential Geometry. Math. Soc. Japan, 1956. Zbl0071.15402MR84166
- [52] N.N. Bogoliubov, J. E. T. P., t, 34, 1958, p. 58.
- [53] F.A. Berezin, The Method of Second Quantization. Acad. Press, 1966. Zbl0151.44001MR208930
- [54] A. Weinstein, Bull. A. M. S., t. 82, 1976, p. 548. Zbl0331.46034MR407595
- [55] K.C. Liu, J. Math. Phys., t. 16, 1975, p. 724 and 2054; t. 17, 1976, p. 859. Zbl0296.46076
- [56] J.P. Eckmann, R. Seneor, Arch. Rational Mechanics, t. 61, 1976, p. 153. Zbl0332.34053MR406147
- [57] V. Arnold, Funct. Anal. and Appl. (russe), t. 6 (II), 1972, p. 12. Zbl0251.70012
- [58] A. Voros, Comptes Rendus « RCP 25 », vol. 22. Univ., Strasbourg, 1975.
- [59] V. Arnold, A. Avez, Problèmes Ergodiques de la Mécanique Classique. Gauthier–Villars, 1967. Zbl0149.21704MR209436
- [60] A.C. Hearn, Reduce User's Manual. Second Edition, University of Utah, 1973.
- [61] A. Voros, An Algebra of Pseudo-differential Operators..., J. Funct. Anal. (to appear). Zbl0386.47031MR496088
- [62] A. Voros, Ph. D. Thesis, Université Paris-Sud (Orsay), May 1977.
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.