Bulletin of the American Mathematical Society

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Book Information:

Author: 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.

Authors: 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.

V. I. Arnol′d, On a characteristic class entering into conditions of quantization, Funkcional. Anal. i Priložen. 1 (1967), 1–14 (Russian). MR 0211415

J. J. Duistermaat, Oscillatory integrals, Lagrange immersions and unfolding of singularities, Comm. Pure Appl. Math. 27 (1974), 207–281. MR 405513, DOI 10.1002/cpa.3160270205

J. J. Duistermaat and L. Hörmander, Fourier integral operators. II, Acta Math. 128 (1972), no. 3-4, 183–269. MR 388464, DOI 10.1007/BF02392165

Victor Guillemin and Shlomo Sternberg, Geometric asymptotics, Mathematical Surveys, No. 14, American Mathematical Society, Providence, R.I., 1977. MR 0516965

Lars Hörmander, Fourier integral operators. I, Acta Math. 127 (1971), no. 1-2, 79–183. MR 388463, DOI 10.1007/BF02392052

Joseph B. Keller, Corrected Bohr-Sommerfeld quantum conditions for nonseparable systems, Ann. Physics 4 (1958), 180–188. MR 99207, DOI 10.1016/0003-4916(58)90032-0

Jean Leray, The meaning of Maslov’s asymptotic method: the need of Planck’s constant in mathematics, Bull. Amer. Math. Soc. (N.S.) 5 (1981), no. 1, 15–27. MR 614311, DOI 10.1090/S0273-0979-1981-14914-4

R. B. Melrose, Equivalence of glancing hypersurfaces, Invent. Math. 37 (1976), no. 3, 165–191. MR 436225, DOI 10.1007/BF01390317

Richard B. Melrose and Michael E. Taylor, Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle, Adv. in Math. 55 (1985), no. 3, 242–315. MR 778964, DOI 10.1016/0001-8708(85)90093-3

11.

M. E. Taylor, Pseudo differential operators, Princeton Univ. Press, Princeton, N. J., 1981.

Alan Weinstein, On Maslov’s quantization condition, Fourier integral operators and partial differential equations (Colloq. Internat., Univ. Nice, Nice, 1974) Lecture Notes in Math., Vol. 459, Springer, Berlin, 1975, pp. 341–372. MR 0436231

13.

H. D. Yingst, The Kirchhoff approximation for Maxwell's equation, Indiana Math. J. (to appear).

1.

V. I. Arnol'd, A characteristic class entering in quantization conditions, Functional Anal. Appl. 1 (1967), 1-14. MR 0211415

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).