Geodesic
The semiclassical limit of eigenfunctions of the Schr\"odinger equation and the Bohr--Sommerfeld quantization condition, revisited
Algebra i analiz, Tome 22 (2010) no. 6, pp. 270-291.

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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 asymptotics of eigenfunctions is justified, and the Bohr–Sommerfeld quantization condition is recovered.
Keywords: Schrödinger equation, potential well, Airy functions, Green–Lioville approximation, Bohr–Sommerfeld quantization condition, semiclassical Weyl formula. 
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D. R. Yafaev. The semiclassical limit of eigenfunctions of the Schr\"odinger equation and the Bohr--Sommerfeld quantization condition, revisited. Algebra i analiz, Tome 22 (2010) no. 6, pp. 270-291. http://geodesic.mathdoc.fr/item/AA_2010_22_6_a11/

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