Semi-classical approximation and microcanonical ensemble

M. Sirugue; M. Sirugue-Collin; A. Truman

Annales de l'I.H.P. Physique théorique (1984)

  • Volume: 41, Issue: 4, page 429-444
  • ISSN: 0246-0211

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Sirugue, M., Sirugue-Collin, M., and Truman, A.. "Semi-classical approximation and microcanonical ensemble." Annales de l'I.H.P. Physique théorique 41.4 (1984): 429-444. <http://eudml.org/doc/76268>.

@article{Sirugue1984,
author = {Sirugue, M., Sirugue-Collin, M., Truman, A.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {semiclassical limit of states; Schrödinger equation; WKB approximation; WKB solution; eigenstates of harmonic oscillator},
language = {eng},
number = {4},
pages = {429-444},
publisher = {Gauthier-Villars},
title = {Semi-classical approximation and microcanonical ensemble},
url = {http://eudml.org/doc/76268},
volume = {41},
year = {1984},
}

TY - JOUR
AU - Sirugue, M.
AU - Sirugue-Collin, M.
AU - Truman, A.
TI - Semi-classical approximation and microcanonical ensemble
JO - Annales de l'I.H.P. Physique théorique
PY - 1984
PB - Gauthier-Villars
VL - 41
IS - 4
SP - 429
EP - 444
LA - eng
KW - semiclassical limit of states; Schrödinger equation; WKB approximation; WKB solution; eigenstates of harmonic oscillator
UR - http://eudml.org/doc/76268
ER -

References

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  1. [1] K.D. Elworthy, A. Truman, Classical Mechanics, The Diffusion (heat). Equation and the Schrödinger Equation on a Riemanian Manifold. J. Math. Phys., t. 22, 1981, p. 2144-2166. Zbl0485.70024MR641455
  2. [2] K.D. Elworthy, A. Truman, The Diffusion Equation and Classical Mechanics: An Elementary Formula. In: Stochastic Processes in Quantum Theory and Statistical Physics. S. ALBEVERIO, Ph. COMBE, M. SIRUGUE-COLLIN, Eds, Lecture Notes in Physics, t. 173, Springer-Verlag, p. 136-146. Zbl0511.60073MR729719
  3. [3] J.P. Eckmann, R. Sénéor, The Maslov-WKB Method for the (an) Harmonic Oscillator. Arch. Rat. Mech. An., t. 61, 1976, p. 153-173. Zbl0332.34053MR406147
  4. [4] T. Arede, S. Albeverio, The Relations between Quantum Mechanics and Classical Mechanics: A Survey of some Mathematical Aspects. Preprint ZiF der Universität Bielefeld, 1983. 
  5. [5] Ph Combe, R. Rodriguez, M. Sirugue, M. Sirugue-Collin, High Temperature Behaviour of Quantum Mechanical Thermal Functionals. Publ. R. I. M. S., Kyoto, t. 19, 1983, p. 355-365. Zbl0528.60060MR700958
  6. [6] L.D. Landau, E.M. Lifshitz, Mechanics. 2nd Ed., Pergamon Press, 1969. 
  7. [7] G. Szegoe, Orthogonal Polynomials. 3rd Ed., Providence, R. J., 1967. 
  8. [8] H. Bateman, Tables of integral transforms. McGraw Hill Book Company, 1954. Lecture at Les Houches, 1981, session XXXVI. Comportement chaotique des systèmes déterministes. G. Ioos, R. H. G. Helleman et R. Stora Ed. North Holland, Amsterdam, 1983. 
  9. [10] V.P. Maslov and M.V. Fedoriuk, Semiclassical Approximation in Quantum Mechanics. Reidel, Dordrecht, 1981 Zbl0458.58001MR634377
  10. [9] M.V. Berry, Semi classical mechanics of regular and irregular motion, p. 171-271. 
  11. [1] M.V. Berry, Philos. Trans. Roy. Soc., London, t. 287, 1977, p. 237-271. Zbl0421.70020MR489464
  12. [2] A.M. Ozorio De Almeida and J.H. Hannay, Ann. Phys., t. 138, 1982, p. 115-154. Zbl0502.70021MR653021
  13. [3] A.M. Ozorio De Almeida, Ann. Phys., t. 145, 1983, p. 100-115. Zbl0517.70020MR696639

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