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Book Review
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Book Information
Author(s):
Jean Leray
Title:
Lagrangian analysis and quantum mechanics, a mathematical structure related to asymptotic expansions and the Maslov index
Additional book information:
the MIT Press, Cambridge, Mass., 1982, xvii + 271 pp., $35.00. ISBN 0-2621-2087-9
Author(s):
V. P. Maslov and M. V. Fedoriuk
Title:
Semi-classical approximation in quantum mechanics
Additional book information:
Mathematical Physics and Applied Mathematics, vol. 7, D. Reidel Publishing Company, Dordrecht:Holland/Boston:U.S.A./London:England, 1981, ix + 294 pp., Cloth Dfl. 125.00/U.S. $66.00. ISBN 9-0277-1219-0
References:
- 1.
- V. I. Arnol'd, A characteristic class entering in quantization conditions, Functional Anal. Appl. 1 (1967), 1-14. MR 211415
- 2.
- J. J. Duistermaat, Oscillatory integrals, lagrange immersions and unfoldings of singularities, Comm. Pure Appl. Math. 27 (1974), 207-281. MR 405513
- 3.
- J. J. Duistermaat and L. Hörmander, Fourier integral operators. II, Acta Math. 128 (1972), 183-269. MR 388464
- 4.
- V. Guillemin and S. Sternberg, Geometric asymptotics, Math. Surveys, no. 14, Amer. Math. Soc., Providence, R. I., 1977. MR 516965
- 5.
- L. Hörmander, Fourier integral operators. I, Acta Math. 127 (1971), 79-183. MR 388463
- 6.
- J. Keller, Corrected Bohr-Sommerfeld quantum conditions for nonseparable systems, Ann. Physics 4 (1958), 100-188. MR 99207
- 7.
- J. Leray, The meaning of Maslov's asymptotic method: the need of Planck's constant in mathematics, Bull. Amer. Math. Soc. (N.S.) 5 (1981), 15-27.8. V. P. Maslov, Perturbation theory and asymptotic methods, Moscow State University, Moscow, 1965; French Transl., Dunod and Gauthier-Villars, Paris, 1972. MR 614311
- 9.
- R. Melrose, Equivalence of glancing hypersurfaces, Invent. Math. 37 (1976), 165-191. MR 436225
- 10.
- R. Melrose and M. E. Taylor, Near peak scattering and the corrected Kirchoff approximation for a convex obstacle, preprint. MR 778964
- 11.
- M. E. Taylor, Pseudo differential operators, Princeton Univ. Press, Princeton, N. J., 1981.
- 12.
- A. Weinstein, On Maslov's quantization condition, Fourier Integral Operators and Partial Differential Equations (J. Chazarain, ed.), Lecture Notes in Math., vol. 459, Springer-Verlag, Berlin and New York, 1975, pp. 341-372. MR 436231
- 13.
- H. D. Yingst, The Kirchhoff approximation for Maxwell's equation, Indiana Math. J. (to appear).
Additional Information:
Reviewer(s):
Robert J.
Blattner
Reviewer(s):
James
Ralston
Review Information:
Journal:
Bull. Amer. Math. Soc.
9
(1983),
387-396.
DOI:
10.1090/S0273-0979-1983-15224-2
PII:
S 0273-0979(1983)15224-2
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