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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
DOI: https://doi.org/10.1090/S0002-9939-1991-1049843-9
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] B. Helffer and D. Robert, Propriétés asymptotiques du spectre d'opérateurs pseudodifferentiels sur $ {R^n}$, Comm. Partial Differential Equations 7 (1982), 795-882. MR 662451 (83j:35127)
  • [2] -, Asymptotique des niveaux d'énergie pour hamiltoniens a un degre de liberté, Duke Math. J. 49 (1982), 853-868. MR 683006 (84m:58144)
  • [3] M. A. Shubin, Pseudodifferential operators and spectral theory, Springer-Verlag, Berlin, 1987. MR 883081 (88c:47105)

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Additional Information

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

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