A probabilistic approach to semi-classical approximations

Journal of Functional Analysis

Volumn 137, Issue 1, 1996, Pages 243-280

  Ben Arous, Gérard ^a   Castell, Fabienne ^b  

^a Lab de Mathematiques de l'Ecole N   (France)

^b UNIVERSITÉ PARIS SUD   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030577873     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1996.0046     Document Type: Article

References (25)

1. 1. S. ALBEVERIO, A. M. BOUTET DE MONVEL BERTHIER, AND Z. BRZEŹNIAK, Stationary phase in infinite dimensions by finite dimensional approximations: Applications to the Schrödinger equation, Potential Anal. 4, No. 5 (1995), 469-502.
2. 2. S. ALBEVERIO AND Z. BRZEŹNIAK, Finite dimensional approximations approach to oscillatory integrals in infinite dimensions, J. Funct. Anal. 113 (1993), 117-244.
3. 3. S. ALBEVERIO AND R. HOEGH-KROHN, "Mathematical Theory of Feynman Path Integrals," Lecture Notes in Math., Vol. 523, Springer-Verlag, Berlin/New York, 1976.
4. 4. V. I. ARNOLD, "Mathematical Methods of Classical Mechanics," Graduate Texts in Mathematics, Springer-Verlag, New York, 1978.
5. eme rencontre franco-allemande entre physiciens et mathématiciens, CIRM, Marseille, 1983," Lecture Notes in Mathematics, Vol. 1109, pp. 1-17, Springer-Verlag, New York/Berlin, 1985.
6. 6. G. BEN AROUS, Méthode de Laplace et de la phase stationnaire sur l'espace de Wiener, Stochastics 25 (1988), 125-153.
7. 7. F. A. BEREZIN AND M. A. SHUBIN, "The Schrödinger Equation," Mathematics and Its Applications, Kluwer, Dordrecht, 1991.
8. 8. H. Doss, "Sur une résolution stochastique de l'équation de Schrödinger à coefficients analytiques," Communications in Mathematical Physics, Vol. 73, pp. 247-264, Springer-Verlag, New York/Berlin, 1980.
9. 9. K. D. ELWORTHY AND A. TRUMAN, Classical mechanics, the diffusion (heat) equation and the Schrödinger equation on a Riemannian manifold, J. Math. Phys. 22 (1981), 2144-2166.
10. 10. R. P. FEYNMAN AND A. R. HIBBS, "Quantum Mechanics and Path Integrals," Mc Graw-Hill, New York, 1965.
11. 11. L. GROSS, Abstract Wiener spaces, in "Fifth Berkeley Symposium," Vol. 2, pp. 31-42.
12. 12. V. GUILLEMIN AND S. STERNBERG, "Geometric Asymptotics," Mathematical Surveys, Vol. 14, Amer. Math. Soc., Providence, RI, 1977.
13. 13. M. C. GÜTZWILLER, "Chaos in Classical and Quantum Mechanics," Springer-Verlag, Berlin, 1990.
14. 14. L. HÖRMANDER, "The Analysis of Partial Differential Operators," Vols. 1-4, Springer-Verlag, New York, 1983-1990.
15. 15. G. KALLIANPUR, D. KANNAN, AND R. L. KARANDIKAR, Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces, and a Cameron Martin formula, Ann. Instil. Poincaré, Probab. Theory 21 (1985), 323-361.
16. 16. H. KUNITA, "Stochastic Flows and Stochastic Differential Equations," Cambridge Studies in Advanced Mathematics, Vol. 24, Cambridge Univ. Press, Cambridge, 1990.
17. 17. V. P. MASLOV, "Theory of Perturbations and Asymptotic Methods," Moskov. Gos. Univ., Moscow, 1965-1970.
18. 18. A. MELIN AND J. SJÖSTRAND, Fourier integral operators with complex-valued phase functions, in "Fourier Integral Operators and Partial Differential Equations," Lecture Notes in Math., Vol. 459, pp. 120-223, Springer-Verlag, New York/Berlin, 1975.
19. 19. D. ROBERT, "Autour de l'approximation semi-classique," Birkhäuser, Bochum, 1987.
20. 20. L. S. SCHULMAN, "Techniques and Applications of Path Integration," Wiley, New York, 1981.
21. 21. D. STROOCK, "An Introduction to the Theory of Large Deviations," Springer-Verlag, New York/Berlin, 1984.
22. 22. F. TREVES, "Introduction to Pseudo-Differential and Fourier Integral Operators," Vol. 2, The University Series in Math., Plenum, New York/London.
23. 23. VAN VLECK, Proc. Natl. Acad. Sci. U.S.A. 14 (1928), 178.
24. 24. A. VOROS, Semi-classical approximations, Ann. Inst. H. Poincaré, Sect. A 24 (1976).
25. 25. S. WATANABE, "Stochastic Differential Equations and Malliavin Calculus," Tata Institute, Bombay/Springer-Verlag, New York/Berlin, 1984.