Semiclassical limit for perturbations of non-resonant rotators
Annales de l'I.H.P. Physique théorique, Volume 52 (1990) no. 4, pp. 377-395.
@article{AIHPA_1990__52_4_377_0,
     author = {Herczy\'nski, Jan},
     title = {Semiclassical limit for perturbations of non-resonant rotators},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {377--395},
     publisher = {Gauthier-Villars},
     volume = {52},
     number = {4},
     year = {1990},
     mrnumber = {1062905},
     zbl = {0699.58059},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1990__52_4_377_0/}
}
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Herczyński, Jan. Semiclassical limit for perturbations of non-resonant rotators. Annales de l'I.H.P. Physique théorique, Volume 52 (1990) no. 4, pp. 377-395. http://archive.numdam.org/item/AIHPA_1990__52_4_377_0/

[1] G. Alvarez, S. Graffi and H. Silverstone, Transition from classical mechanics to quantum mechanics: x4 perturbed harmonic oscillator, Phys. Rev. A (to appear).

[2] G. Benettin, L. Galgani and A. Giorgilli, Classical perturbation theory for systems of weakly coupled rotators, Il Nuovo Cimento, 89 B, 1985, 89-102. | MR

[3] M. Born, Atomic Mechanics, Bell, London 1960.

[4] L. Chierchia and G. Gallavotti, Smooth prime integrals for quasi-integrable Hamiltonian systems, Il Nuovo Cimento, 67B, 1982, 277-295. | MR

[5] G. Gallavotti, The elements of mechanics, Berlin, Heidelberg, New York: Springer, 1983. | MR | Zbl

[6] S. Graffi and T. Paul, The Schrödinger equation and canonical perturbation theory, Commun. Math. Phys, 108, 1987, 25-40. | MR | Zbl

[7] S. Graffi, T. Paul and H. Silverstone, Classical resonance overlapping and quantum avoided crossings, Phys. Rev. Lett., 59, 1987, 255-258.

[8] S. Graffi, T. Paul and H. Silverstone, Resonance overlapping in classical mechanics and avoided crossings in quantum mechanics, CPT preprint P. 2025, 1987. | MR

[9] L. Hörmander, The Analysis of linear partial differential operators, Berlin, Heidelberg, New York: Springer, 1983. | MR

[10] V.V. Kozlov and D.V. Treščov, On integrability of Hamiltonian systems with toroidal configuration space, Mat. Sbornik, 135, 1988, 119-138 (in Russian). | Zbl

[11] A. Messiah, Quantum mechanics, North-Holland, Amsterdam 1961. | MR | Zbl

[12] M. Reed and B. Simon, Methods of modern mathematical physics, IV, New York: Academic Press, 1978. | MR | Zbl

[13] G. Turchetti, Classical limit and Stieltjes property of perturbation series for classical anharmonic oscillators, Il Nuovo Cimento, 82B, 1984, 203-217. | MR

[14] C.E. Wayne, Bounds on the trajectories of a system of weakly coupled rotators, Commun. Math. Phys., 104, 1986, 21-36. | MR | Zbl

[15] A. Voros, The return of the quartic oscillator, Ann. Inst. Henri Poincaré, 39, 1983, 211-338. | Numdam | MR | Zbl