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arXiv · 2505.05342

Rigorous Methods for Bohr-Sommerfeld Quantization Rules

Joanne Dong·Peter D. Miller·Giorgio Young
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Abstract

In this work, we prove Bohr-Sommerfeld quantization rules for the self-adjoint Zakharov-Shabat system and the Schr\"odinger equation in the presence of two simple turning points bounding a classically allowed region. In particular, we use the method of comparison equations for $2\times 2$ 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.

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Joanne Dong, Peter D. Miller, Giorgio Young. 2025-05-08. Rigorous Methods for Bohr-Sommerfeld Quantization Rules. https://arxiv.org/abs/2505.05342

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