@article{AIHPA_1983__39_3_211_0, author = {Voros, A.}, title = {The return of the quartic oscillator. {The} complex {WKB} method}, journal = {Annales de l'I.H.P. Physique th\'eorique}, pages = {211--338}, publisher = {Gauthier-Villars}, volume = {39}, number = {3}, year = {1983}, mrnumber = {729194}, zbl = {0526.34046}, language = {en}, url = {http://archive.numdam.org/item/AIHPA_1983__39_3_211_0/} }
TY - JOUR AU - Voros, A. TI - The return of the quartic oscillator. The complex WKB method JO - Annales de l'I.H.P. Physique théorique PY - 1983 SP - 211 EP - 338 VL - 39 IS - 3 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPA_1983__39_3_211_0/ LA - en ID - AIHPA_1983__39_3_211_0 ER -
Voros, A. The return of the quartic oscillator. The complex WKB method. Annales de l'I.H.P. Physique théorique, Tome 39 (1983) no. 3, pp. 211-338. http://archive.numdam.org/item/AIHPA_1983__39_3_211_0/
[1] Phys. Rev. Lett., t. 41, 1978, p. 1141.
, , ,[2] « Quartic Oscillator », in Feyman Path Integrals (Proceedings, Marseille, 1978), Springer Lecture Notes in Physics, t. 106, 1979. | MR | Zbl
, , ,[3] Nucl. Phys., t. B 165, 1980, p. 209 (updated text in [39], p. 184).
,[4] Asymptotic Expansions: Their Derivation and Interpretation, Acad. Press, 1973. | MR | Zbl
,[5] Asymptotics and Special Functions, Acad. Press, 1974. | MR | Zbl
,[6] Rep. Progr. Phys., t. 35, 1972, p. 315.
, ,[7] Ann. Phys., t. 97, 1976, p. 307. | MR
, ,[8] Méthode de la Phase Stationnaire et Sommation de Borel, in Ref. [28], p. 170 ; | MR | Zbl
,Proceedings of the 1981 Summer Institute on Singularities, (Arcata, California) to appear in Proc. Symposia Pure Math. (AMS).
, in :[9] Phys. Rev., t. D 19, 1979, p. 2370.
,[10] Generalized Functions, t. 1, Acad. Press, 1968.
, ,[11] Ann. Phys., t. 85, 1974, p. 514. | MR | Zbl
, ,[12] Mécanique Quantique, t. 1, Dunod, 1959 ; English Translation: North Holland, 1961. | MR
,[13] An Introduction to Phase-Integral Methods, Methuen, 1962 ; , , JWKB Approximation : Contribution to the Theory, North Holland, 1965. | MR | Zbl
,[14] Spectre de l'Équation de Schrödinger et Méthode BKW, Lecture Notes, Publications mathématiques d'Orsay, t. 81-09, Université Paris-Sud, 1981. | Zbl
,[15] Eigenfunction Expansions, t. 1, Oxford Univ. Press, 1961.
,[16] Phys. Rev., t. 82, 1951, p. 840. | MR | Zbl
, ,[17] Ark. Fys., t. 32, 1966, p. 541.
,[18] Phys. Rev., t. 41, 1932, p. 713, 721. | Zbl
,[19] J. Math. Pures et Appl., t. 55, 1976, p. 297. | MR | Zbl
, , ,[20] Asymptotic Expansions for Ordinary Differential Equations, Interscience, Wiley, 1965. | MR | Zbl
,[21] Publ. Math. IHES, t. 46, 1976, p. 163. | Numdam | MR | Zbl
,[22] For instance: I11-Condensed Matter, Les Houches, 1978, Proceedings, North Holland, 1979.
, Course 4, in : R. BALIAN et al. (eds):[23] J. Chem. Phys., t. 47, 1967, p. 2942 , , , , Phys. Rev., t. D 16, 1977, p. 1740.
, , ,[24] For instance: Phys. Rev., t. B 21, 1980, p. 3976. | Zbl
, ,[25] Leçons sur les Progrès Récents de la Théorie des Séries de Dirichlet, Gauthier-Villars, 1933. | JFM | Zbl
,[26] Topology, t. 4, 1965, p. 159 ; | MR | Zbl
, , , ,Homology and Feynman Integrals, Benjamin, 1966 ; | MR | Zbl
, ,Introduction à I'Étude Topologique des Singularités de Landau, Gauthier-Villars, 1967 ; | MR | Zbl
,Comm. Math. Phys., t. 15, 1969, p. 83. | MR | Zbl
, , , ,[27] For instance: Knots and Links, Publish or Perish, 1976. | MR
,[28] Complex Analysis, Microlocal Calculus and Relativistic Quantum Theory, Springer Lecture Notes in Physics, t. 126, 1980. | MR | Zbl
(ed.),[29] Invent. Math., t. 24, 1974, p. 65 ; , , Invent. Math., t. 29, 1975, p. 39. | MR | Zbl
,[30] Phys. Reports, t. 57, 1980, p. 47. | MR
,[31] For instance: J. Math. Phys., t. 22, 1981, p. 511 (Appendix A).
,[32] Les Fonctions Résurgentes, Publications Mathématiques de l'Université Paris-Sud, t. 81-05 and 81-06, Orsay, 1981. | Zbl
,[33] The Analytic S-Matrix, Benjamin, 1966 ; , . and , The Analytic S-Matrix. Cambridge University Press, 1966 ; , The S-Matrix, North Holland, 1978. | MR
,[34] C. R. Acad. Sci., t. 293, Série I, 1981, p. 709 (in English: J. Physique-Lettres. t. 43, 1982, p. L-1). | MR | Zbl
,[35]
, preprint, 1978, reprinted in [39], p. 178.[36] Handbook of Mathematical Functions, Chap. 23, NBS, 1964, Dover, 1965.
, ,[37] Higher Transcendental Functions (Bateman Manuscript Project) t. 2, McGraw Hill, 1953. | Zbl
et al.,[38] Generalized Hypergeometric Functions, Cambridge University Press, 1966. | MR | Zbl
,[39] The Riemann Problem..., Springer Lecture Notes in Mathematics, t. 925, 1982.
and (eds.),[40] Symposium on Ordinary Differential Equations, Springer Lecture Notes in Mathematics, t. 312, 1973 ; , Global Theory of a Second Order Linear Ordinary Differential Operator with a Polynomial Coefficient, Chap. V, North Holland, 1975. | MR
and , in : and (eds.),[41] Séminaire Bourbaki, 1982-1983, Lecture n° 602, nov. 1982, to be published by Astérisque, Soc. Math. de France, 1983. | Numdam | Zbl
,[42] Transformées de Laplace des Microsolutions de Systèmes Holonomes, submitted to: L'Enseignement Mathématique, and: Calcul Microdifferentiel Complexe et Méthode Semi-Classique, 36e Rencontre RCP 25, May 1983 (to appear in the Proceedings, IRMA, Strasbourg). | MR
,