Problème spectral de Sturm-Liouville : le cas de l'oscillateur quartique

André Voros

Séminaire Bourbaki (1982-1983)

  • Volume: 25, page 95-104
  • ISSN: 0303-1179

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Voros, André. "Problème spectral de Sturm-Liouville : le cas de l'oscillateur quartique." Séminaire Bourbaki 25 (1982-1983): 95-104. <http://eudml.org/doc/110019>.

@article{Voros1982-1983,
author = {Voros, André},
journal = {Séminaire Bourbaki},
keywords = {fourth order potential; semiclassical approach},
language = {fre},
pages = {95-104},
publisher = {Société Mathématique de France},
title = {Problème spectral de Sturm-Liouville : le cas de l'oscillateur quartique},
url = {http://eudml.org/doc/110019},
volume = {25},
year = {1982-1983},
}

TY - JOUR
AU - Voros, André
TI - Problème spectral de Sturm-Liouville : le cas de l'oscillateur quartique
JO - Séminaire Bourbaki
PY - 1982-1983
PB - Société Mathématique de France
VL - 25
SP - 95
EP - 104
LA - fre
KW - fourth order potential; semiclassical approach
UR - http://eudml.org/doc/110019
ER -

References

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  1. [1] E.C. Titchmarsh, Eigenfunction Expansions, vol.1, Oxford University Press, 1961. Zbl0106.27902
  2. [2] M.V. Berry, K. Mount, Rep. Prog. Phys.35(1972), 315 (article de revue). 
  3. [3] N. Fröman, P. Fröman, JWKB Approximation : Contribution to the Theory, North-Holland, 1965. F.W.J. Olver, Asymptotics and Special Functions, Acad. Press, 1974. Zbl0129.41907MR173481
  4. [4] R.B. Dingle, Asymptotic Expansions : Their Derivation and Interpretation, Acad. Press, 1973. Zbl0279.41030MR499926
  5. [5] R. Balian, C. Bloch, Ann. Phys.85(1974), 514. Zbl0281.35029MR438937
  6. [6] V.P. Maslov, Théorie des Perturbations et Méthodes Asymptotiques, Dunod, 1972. Zbl0247.47010
  7. J.J. Duistermaat, V. Guillemin, Invent. Math.29(1975), 39. Zbl0307.35071MR405514
  8. J. Leray, Analyse Lagrangienne et Mécanique Quantique, Collège de France, 1976, et IRMAStrasbourg, 1978, n° 10/P-03 (traduction anglaise : MIT Press, 1982). MR501198
  9. J. Chazarain, Comm. in PDE5(1980), 595. MR578047
  10. [7] L. Hörmander, Arkiv för Mat.17(1979), 297. MR608322
  11. B. Helffer, D. Robert, C.R.A.S.292, Série I(1981), 47, et Ann. Scuola Norm. Sup. Pisa (à paraître). MR610145
  12. [8] A. Voros, The Return of the Quartic Oscillator, Prétirage Saclay D.Ph-T/81-48, soumis aux Ann. Inst. H. Poincaré (série A), et C.R.A.S.293, Série I(1981), 709. (Version anglaise : J. Physique-Lettres43(1982), L-1.) Zbl0526.34046
  13. [9] C.M. Bender, K. Olaussen, P.S. Wang, Phys. Rev. D16(1977), 1740. MR456017
  14. R. Balian, G. Parisi, A. Voros, Quartic Oscillator, dans : S. Albeverio et al. (eds), Feynman Path Integrals, Springer, Lecture Notes in Physics, vol. 106 (1979), 337. Zbl0417.34094MR553093
  15. [10] A. Voros, Nucl. Phys. B165(1980), 209, et dans [16], p. 184. 
  16. [11] C.E. Reid, J. Molec. Spectrosc.36(1970), 183. 
  17. [12] Y. Hamada, J. Leray, C. Wagschal, J. Math. Pures et Appl.55(1976), 297. Zbl0307.35056MR435614
  18. [13] D. Fotiadi, M. Froissart, J. Lascoux, F. Pham, Topology4(1965), 159. Zbl0173.09301MR214101
  19. [14] G. Ponzano, T. Regge, E.R. Speer, M.J. Westwater, Comm. Math. Phys.15(1969), 83. MR253661
  20. [15] J. Écalle, Les fonctions résurgentes, Publications Mathématiques de l'Université Paris-Sud vol. 81-05 et 81-06, Orsay, 1981. Zbl0499.30035
  21. [16] D. Chudnovsky, G. Chudnovsky (eds.), The Riemann Problem..., Springer, Lecture Notes in Maths. vol. 925(1982). 
  22. [17] Y. Sibuya, Global Theory of a second Order Linear Ordinary Differential Equation with a Polynomial Coefficient, chap. V, North-Holland, 1975. Zbl0322.34006MR486867
  23. [18] J. Knoll, R. Schaeffer, Ann. Phys.97(1976), 307. MR408530
  24. [19] G. Parisi, dans [16], p. 178. 
  25. [20] D. Widder, The Laplace Transform, chap. V, Princeton University Press, 1946. Zbl0060.24801MR5923JFM67.0384.01

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