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Rigorous methods for Bohr-Sommerfeld quantization rules
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DOI：10.4171/emss/114.png)
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Abstract
En 中文
In this paper, we will prove Bohr-Sommerfeld quantization rules for the self-adjoint Zakharov-Shabat system and the Schr & ouml;dinger equation in the presence of two simple turning points bounding a classically allowed region. In particular, we use the method of comparison equations for 2x2 traceless first-order systems to provide a unified perspective that yields similar proofs in each setting. The use of a Weber model system gives results that are uniform in the eigenvalue parameter over the whole range from the bottom of the potential well up to finite values.
Keywords:
WKBJ method
Bohr-Sommerfeld quantization
stationary Schr & ouml
dinger equations
Zakharov-Shabat systems
Journal
E
IF:
1.2
Papers:
12
Citations:
0