The semiclassical limit of eigenfunctions of the Schrödinger equation and the Bohr–Sommerfeld quantization condition, revisited
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- by D. R. Yafaev
- St. Petersburg Math. J. 22 (2011), 1051-1067
- DOI: https://doi.org/10.1090/S1061-0022-2011-01183-5
- Published electronically: August 22, 2011
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Abstract:
The semiclassical limit, as the Planck constant $\hbar$ tends to $0$, of bound states of a quantum particle in a one-dimensional potential well is considered. The semiclassical asymptotic formulas for eigenfunctions are justified, and the Bohr–Sommerfeld quantization condition is recovered.References
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Bibliographic Information
- D. R. Yafaev
- Affiliation: Irmar, Université de Rennes I, Campus de Beaulieu, 35042 Rennes Cedex, France
- Email: yafaev@univ-rennes1.fr
- Received by editor(s): August 5, 2010
- Published electronically: August 22, 2011
- Additional Notes: Partially supported by the project NONAa, ANR-08-BLANC-0228
- © Copyright 2011 American Mathematical Society
- Journal: St. Petersburg Math. J. 22 (2011), 1051-1067
- MSC (2010): Primary 47A40, 81U05
- DOI: https://doi.org/10.1090/S1061-0022-2011-01183-5
- MathSciNet review: 2760094
Dedicated: To Vasiliĭ Mikhaĭlovich Babich on his 80th birthday