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St. Petersburg Mathematical Journal

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The semiclassical limit of eigenfunctions of the Schrödinger equation and the Bohr-Sommerfeld quantization condition, revisited

Author: D. R. Yafaev
Original publication: Algebra i Analiz, tom 22 (2010), nomer 6.
Journal: St. Petersburg Math. J. 22 (2011), 1051-1067
MSC (2010): Primary 47A40, 81U05
Published electronically: August 22, 2011
MathSciNet review: 2760094
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Abstract | References | Similar Articles | Additional Information

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.

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Additional Information

D. R. Yafaev
Affiliation: Irmar, Université de Rennes I, Campus de Beaulieu, 35042 Rennes Cedex, France

Keywords: Schrödinger equation, potential well, Airy functions, Green–Liouville approximation, Bohr–Sommerfeld quantization condition, semiclassical Weyl formula
Received by editor(s): August 5, 2010
Published electronically: August 22, 2011
Additional Notes: Partially supported by the project NONAa, ANR-08-BLANC-0228
Dedicated: To Vasiliĭ Mikhaĭlovich Babich on his 80th birthday
Article copyright: © Copyright 2011 American Mathematical Society