Semi-classical approximations

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1. [1] A. Messiah, Mécanique Quantique, Dunod, Paris, 1965. MR129304
2. [2] L. Landau et E. Lifschitz, Mécanique Quantique, Mir, Moscow. 
3. [3] L. Landau et E. Lifschitz, Mécanique, Mir, Moscow. 
4. [4] L. Janossy, Found of Physics, t. 3, 1973, p. 185. MR449257
5. [5] J.B. Keller, Ann. Phys., t. 4, 1958, p. 180. Zbl0085.43103MR99207
6. [6] D. Ludwig, Comm. Pure Appl. Math., t. 13, 1960, p. 473. Zbl0098.29601MR115010
7. [7] J.B. Keller and S. Rubinow, Phys. Rev., t. 131, 1963, p. 2789. MR159575
8. [8] J. Milnor, Morse Theory . Princeton Univ. Press, 1963. Zbl0108.10401MR163331
9. [9] E. Wigner, Phys. Rev., t. 40, 1932, p. 749 ; K. Imre et al., J. Math. Phys., t. 8, 1967, p. 1097 ; A. Grossmann, G. Loupias and E.M. Stein, Ann. Inst. Fourier, t. 18, 1969, p. 343. 
10. [10] V. Maslov, Théorie des Perturbations. Dunod, Paris, 1972 : this French translation (by J. Lascoux and R. Seneor) includes the articles of ref. [11]. Zbl0247.47010
11. [11] V. Arnold, Funct. Anal., t. 1, 1967, p. 1 ; V. Bouslaiev, Funct. Anal., t. 3, 1969, p. 17 (in Russian, see ref. [10]). 
12. [12] J. Leray, Proc. « RCP 25 », vol. 18, Strasbourg University, publ. 1973. 
13. [13] V. Arnold and A. Avez, Problèmes Ergodiques de la Mécanique Classique. Gauthier-Villars, Paris, 1967. Zbl0149.21704MR209436
14. [14] H. Poincaré, Méthodes Nouvelles de la Mécanique Céleste. Gauthier-Villars, Paris, 1892; A.T. Whittaker, Treatise on Analytical Dynamics. Cambridge, Univ. Press, 1959. 
15. [15] K. Hepp, Comm. Math. Phys., t. 35, 1974, p. 265. MR332046
16. [16] R. Balian and C. Bloch, Ann. Phys., t. 60, 1970, p. 401 ; t. 63, 1971, p. 592; t. 64, 1971, p. 271 ; t. 69, 1972, p. 76. Zbl0207.40202
17. [17] R. Balian and C. Bloch, Ann. Phys., t. 85, 1974, p. 514. Zbl0281.35029MR438937
18. [18] M.C. Gutzwiller, J. Math. Phys., t. 11, 1970, p. 1791 ; t. 12, 1971, p. 343, and references therein. 
19. [19] R. Feynman and A. Hibbs, Quantum Mechanics and Path Integrals. McGraw-Hill, 1965. Zbl0176.54902
20. [20] I. Fenyes, Z. Phys., t. 132, 1952, p. 81 ; E. Nelson, Dynamical Theories of Brownian Motion. Princeton Univ. Press, 1972. MR56458
21. [21] For instance: J. Heading, Introduction to Phase Integral Methods. Methuen, London, 1967 ; N. Fröman and P. Fröman, JWKB approximation. North Holland, 1965. Zbl0129.41907
22. [22] M. Berry and K. Mount, Rep. Prog. Phys., t. 35, 1972, p. 315. 
23. [23] R. Abraham and J. Marsden, Foundations of Mechanics. Benjamin, 1967. 
24. [24] J.M. Souriau, Structure des Systèmes Dynamiques. Dunod, Paris, 1970. Zbl0186.58001MR260238
25. [25] C. Godbillon, Géométrie Différentielle et Mécanique Analytique. Hermann, Paris, 1971. MR242081
26. [26] R. Courant and D. Hilbert, Methods of Mathematical Physics. II. Interscience, 1962. Zbl0099.29504
27. [27] H. Weyl and H. Robertson, The Theory of Groups and Quantum Mechanics. Dover. Zbl55.0247.02
28. [28] L. Hörmander, L'Enseignement Mathématique, t. 17, 1971, p. 99 ; L. Hörmander, Acta Math., t. 127, 1971, p. 79 ; L. Hörmander and J. Duistermaat, Acta Math., t. 128, 1972, p. 183. MR331124
29. [29] D. Iagolnitzer, Introduction to S-Matrix Theory. ADT, Paris, 1973. 
30. [30] K. Hepp and E. Lieb, in Constructive Field Theory. Springer Lecture Notes in Physics, t. 25, 1973. MR395513
31. [31] L. Schwartz, Distributions. Hermann, 1957 ; K. Yosida, Functional Analysis, chap. 1, Springer, 1968. MR107812
32. [32] J.P. Eckmann and R. Seneor, The Maslov-WKB Method for the Harmonic Oscillator. To appear in Arch. Rational Mechanics. Zbl0332.34053MR406147
33. [33] For instance: H. Abarbanel, Cargèse Lectures , vol. 5. Gordon and Breach, 1972. 
34. [34] A.I. Khinchin, Mathematical Foundations of Statistical Mechanics. Dover, 1949. Zbl0037.41102MR29808
35. [35] I.E. Farquhar, Ergodic Theory in Statistical Mechanics. Interscience, 1964. MR178893
36. [36] V. Arnold, Funct. Anal. and Applications (Russian), t. 6 (II), 1972, p. 12. Zbl0251.70012
37. [37] V. Lazutkin, Izv. Akad. Nauk USSR (Math.), t. 37, 1973, p. 186 and 437 and references therein. Zbl0256.52001
38. [38] J.B. Keller and S. Rubinov, Ann. Phys., t. 9, 1960, p. 24. Zbl0087.43002
39. [39] S. Sternberg, Celestial Mechanics. II. Benjamin, 1969. Zbl0194.56702
40. [40] A. Voros, Proc. « RCP 25 », vol. 18. Strasbourg University, publ. 1973. 
41. [41] A.J. Hanson and T. Regge, IAS. Princeton preprint, 1974. MR351335
42. [42] B. Kostant, Springer Lecture Notes in Mathematics, t. 170, 1970 ; P. Renouard, Thesis, Orsay, 1969. MR276413
43. [43] For instance: Proc. of the 1974 Conference of Mathematical Physics. Warsaw, to be published ; E. ONOFRI et M. PAURI, J. Math. Phys., t. 13, 1972, p. 533 and references therein. 
44. [44] Y. Colin De Verdière, Compositio Math., t. 3, 1973 ; J. Chazarain, C. R. Acad. Sci. Paris, t. 277, 1973, p. 595 ; J. Duistermaat and V. Guillemin, Proc. Symp. Diff. Geometry, August 1973, Stanford. 
45. [45] T. Kato, Perturbation Theory. Springer, 1966, p. 443. Zbl0148.12601
46. [46] For instance: Y. Iwasaki, Prog. Theor. Phys., t. 46, 1971, p. 1587. 
47. [47] I.M. Gelfand and F. Chilov, Generalized Functions. Academic Press, 1968. Zbl0159.18301
48. [48] For instance, J. Iliopoulos, C. Itzykson and A. Martin, Saclay preprint DPh-T/74-18. 
49. [49] M. Abramowitz and I. Stegun, Handbook of Mathematical Functions. Dover, 1970. 
50. [50] I.C. Percival, J. Phys. (Letters), B 6, 1973, L229. 
51. [51] G.W. Mackey, Mathematical Foundations of Quantum Mechanics. Benjamin, 1963. Zbl0114.44002
52. [52] I.M. Gelfand and V.B. Lidski, Usp. Mat. Nauk, t. 10-1, 1955, p. 3 and A. M. S. Translations, t. 8, 1958, p. 143. Zbl0064.08901
53. [53] A. Voros, Proc. « Colloque Symplectique ». Aix-en-Provence, June 1974, to be published by the C. N. R. S., Paris. 
54. [54] A. Voros, Proc. « RCP 25 » of May1975, Strasbourg University (to appear).