Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Creation and annihilation operators for anharmonic oscillators


Author: Leonid Friedlander
Journal: Proc. Amer. Math. Soc. 113 (1991), 425-433
MSC: Primary 47G30; Secondary 35S99, 47E05, 81S05
MathSciNet review: 1049843
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Abstract: Positive elliptic operators from the Helffer-Robert classes of pseudodifferential operators on the line can be approximately factored as products of creation and annihilation operators. Operators of anharmonic oscillators belong to these classes.


References [Enhancements On Off] (What's this?)

  • [1] Bernard Helffer and Didier Robert, Propriétés asymptotiques du spectre d’opérateurs pseudodifférentiels sur 𝑅ⁿ, Comm. Partial Differential Equations 7 (1982), no. 7, 795–882 (French). MR 662451, 10.1080/03605308208820239
  • [2] B. Helffer and D. Robert, Asymptotique des niveaux d’énergie pour des hamiltoniens à un degré de liberté, Duke Math. J. 49 (1982), no. 4, 853–868 (French). MR 683006
  • [3] M. A. Shubin, Pseudodifferential operators and spectral theory, Springer Series in Soviet Mathematics, Springer-Verlag, Berlin, 1987. Translated from the Russian by Stig I. Andersson. MR 883081

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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1049843-9
Article copyright: © Copyright 1991 American Mathematical Society