@article{AIHPA_1977__26_4_343_0, author = {Voros, A.}, title = {Asymptotic $\hbar $-expansions of stationary quantum states}, journal = {Annales de l'institut Henri Poincar\'e. Section A, Physique Th\'eorique}, pages = {343--403}, publisher = {Gauthier-Villars}, volume = {26}, number = {4}, year = {1977}, mrnumber = {456138}, language = {en}, url = {http://www.numdam.org/item/AIHPA_1977__26_4_343_0/} }
TY - JOUR AU - Voros, A. TI - Asymptotic $\hbar $-expansions of stationary quantum states JO - Annales de l'institut Henri Poincaré. Section A, Physique Théorique PY - 1977 SP - 343 EP - 403 VL - 26 IS - 4 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPA_1977__26_4_343_0/ LA - en ID - AIHPA_1977__26_4_343_0 ER -
%0 Journal Article %A Voros, A. %T Asymptotic $\hbar $-expansions of stationary quantum states %J Annales de l'institut Henri Poincaré. Section A, Physique Théorique %D 1977 %P 343-403 %V 26 %N 4 %I Gauthier-Villars %U http://www.numdam.org/item/AIHPA_1977__26_4_343_0/ %G en %F AIHPA_1977__26_4_343_0
Voros, A. Asymptotic $\hbar $-expansions of stationary quantum states. Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Volume 26 (1977) no. 4, pp. 343-403. http://www.numdam.org/item/AIHPA_1977__26_4_343_0/
[1] Mécanique Quantique. Dunod, Paris, 1965. | MR
,[2] Mécanique Quantique, Mir (Moscow).
- ,[3] Ann. Phys., t. 4, 1958, p. 180. | MR | Zbl
,[4] Théorie des Perturbations. Dunod, Paris, 1972 (translated by J. LASCOUX and R. SÉNÉOR, includes refs. [45] [46]).
,[5] Methods of Mathematical Physics II. Interscience, 1962. | Zbl
, ,[6] Comm. Pure Appl. Math., t. 13, 1960, p. 473. | MR | Zbl
,[7] Acta Math., t. 127, 1971, p. 79; , , Acta Math., t. 128, 1972, p. 183. | MR | Zbl
,[8] Fourier Integral Operators. Courant Institute Press, 1973. | MR | Zbl
,[9] Fourier Integral Operators and Partial Differential Equations (Proc. 1974, Conference, Nice). Springer Lecture Notes in Mathematics, vol. 459, 1975. | MR | Zbl
,[10] H. Hyperfunctions and Pseudo-differential Equations. Springer Lecture Notes in Mathematics, vol. 287, 1973 ; , Hyperfunctions and | MR | Zbl
,Theoretical Physics. Springer Lectures Notes in Mathematics, vol. 449, 1975 ; , , Ann. Inst. H. Poincaré, t. 18, 1973, p. 147 and Séminaire Goulaouic-Lions-Schwartz, Lecture n° 18, 1975. | Numdam
[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. | MR
[12] Comm. Pure Appl. Math., t. 27, 1974, p. 207. | MR | Zbl
,[13] Geometric Asymptotics. A. M. S., to appear. | Zbl
, ,[14] Phys. Rev., t. 40, 1932, p. 749; , J. Math. Phys., t. 7, 1966, p. 66; et al., J. Math. Phys., t. 8, 1967, p. 1097.
,[15] Ann. Inst. Fourier, t. 18, 1969, p. 343. | Numdam | MR | Zbl
, , ,[16] Physica, t. 12, 1946, p. 405 ; , Proc. Cambridge Phil. Soc., t. 45, 1949, p. 99; , The Poisson-Moyal Bracket. Harvard University, Physics Dept. preprint, 1976. | MR
,[17] Comm. Math. Phys., t. 1, 1965, p. 14 ; , , Comm. Math. Phys., t. 2, 1966, p. 31. | MR | Zbl
,[18] Proc. Roy. Soc., t. A 235, 1956, p. 419. | MR | Zbl
, ,[19] Phys. Rev., t. 121, 1961, p. 1704 ; , , Ann. Phys., t. 63, 1971, p. 592. | MR
, ,[20] Quantum Mechanics and Path. Integrals. McGraw Hill, 1965; , Comm. Math. Phys., t. 28, 1972, p. 47 and t. 37, 1974, p. 63. | Zbl
, ,[21] Ann. Phys., t. 60, 1970, p. 401 ; t. 64, 1971, p. 271 ; t. 69, 1972, p. 76. | Zbl
, ,[22] Rep. Prog. Phys., t. 35, 1972, p. 315.
, ,[23]
, in [9] [11].[24] Comm. Math. Phys., t. 1, 1966, p. 374 and Structure des Systèmes Dynamiques. Dunod, Paris, 1970. | MR
,[25] 170, 1970. | MR
, in Springer Lecture Notes in Mathematics, vol.[26] Mathematical Physics and Physical Mathematics. Proc., 1974, Conference, Warsaw, Reidel, 1976. | MR | Zbl
, ,[27] Ann. Inst. H. Poincaré, t. 24, 1976, p. 31. | Numdam | MR
,[28] Compositio Math., t. 27, 1973, p. 159. | Numdam | MR | Zbl
,[29] Quasi-Modes sur les Variétés Riemanniennes. Preprint, Paris VII University. | MR
,[30] Inventiones Math., t. 29, 1975, p. 39. | MR | Zbl
, ,[31] J. Math. Phys., t. 12, 1971, p. 343 ; , in [11]; , , , Phys. Rev., t. D 10, 1974, p. 4114 and t. D 11, 1975, p. 3424.
,[32]
, in [11].[33] Symposia Math., t. 14, 1974, p. 139; , , - BERG, in [11].
,[34] Acad. Roy. Belg. Bull. Class. Sci., t. 37, 1951, p. 610. | MR | Zbl
,[35] Mat. Fys. Medd. Danske Vid. Selk., t. 31, 1959, p. 1; , Trans. A. M. S., t. 103, 1962, p. 149; , Acta Math., t. 111, 1963, p. 143. | MR
,[36] Mécanique, Mir. Moscow.
, ,[37] Foundations of Mechanics. Benjamin, 1967. | Zbl
, ,[38] Mathematical Foundations of Quantum Mechanics. Benjamin, 1967.
,[39] Théorie des Distributions. Hermann, 1957. | MR | Zbl
,[40] Methods of Modern Mathematical Physics. Academic Press, 1972 and 1975. | MR
, ,[41] Theory of Groups and Quantum Mechanics. Dover.
, ,[42] Funct. Anal. and Appl. (Russian), t. 4 (3), 1970, p. 37; , Comm. Pure Appl. Math., t. 27, 1974, p. 585. | Zbl
,[43] Hypoellipticity and Eigenvalue Asymptotics. Lecture Notes in Mathematics. Springer, 1975, p. 464. | MR | Zbl
,[44] Private communication.
,[45] Funct. Anal. and Appl. (russe), t. 1, 1967, p. 1 ; translated in [4].
,[46] Funct. Anal. and Appl. (russe), t. 3, 1969, p. 17; translated in [4].
,[47] J. Math. Phys., t. 12, 1971, p. 1772. | MR | Zbl
, ,[48] Induced Representations of Groups and Quantum Mechanics. Benjamin, 1968. | MR | Zbl
,[49] In 4th Colloquium on Group Theoretical Methods in Physics. Univ. Nijmegen, 1975.
,[50] Generalized Functions IV. Academic Press, 1964.
, ,[51] Lie Groups and Differential Geometry. Math. Soc. Japan, 1956. | MR | Zbl
,[52] J. E. T. P., t, 34, 1958, p. 58.
,[53] The Method of Second Quantization. Acad. Press, 1966. | MR | Zbl
,[54] Bull. A. M. S., t. 82, 1976, p. 548. | MR | Zbl
,[55] J. Math. Phys., t. 16, 1975, p. 724 and 2054; t. 17, 1976, p. 859. | Zbl
,[56] Arch. Rational Mechanics, t. 61, 1976, p. 153. | MR | Zbl
, ,[57] Funct. Anal. and Appl. (russe), t. 6 (II), 1972, p. 12. | Zbl
,[58] Comptes Rendus « RCP 25 », vol. 22. Univ., Strasbourg, 1975.
,[59] Problèmes Ergodiques de la Mécanique Classique. Gauthier-Villars, 1967. | MR | Zbl
, ,[60] Reduce User's Manual. Second Edition, University of Utah, 1973.
,[61] An Algebra of Pseudo-differential Operators..., J. Funct. Anal. (to appear). | MR | Zbl
,[62] Ph. D. Thesis, Université Paris-Sud (Orsay), May 1977.
,