Creation and annihilation operators for anharmonic oscillators
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- by Leonid Friedlander PDF
- Proc. Amer. Math. Soc. 113 (1991), 425-433 Request permission
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
- Bernard Helffer and Didier Robert, Propriétés asymptotiques du spectre d’opérateurs pseudodifférentiels sur $\textbf {R}^{n}$, Comm. Partial Differential Equations 7 (1982), no. 7, 795–882 (French). MR 662451, DOI 10.1080/03605308208820239
- 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
- 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, DOI 10.1007/978-3-642-96854-9
Additional Information
- © Copyright 1991 American Mathematical Society
- 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