标题： 玻尔-索末菲量子化规则的严格方法 显示英文标题

标题： Rigorous Methods for Bohr-Sommerfeld Quantization Rules

摘要： 在这项工作中，我们证明了自伴的Zakharov-Shabat系统和具有两个简单转向点的经典允许区域的薛定谔方程的玻尔-索末菲量子化规则。特别是，我们使用比较方程方法处理迹零的一阶系统$2\times 2$，以提供统一的观点，在每种设定下都能得出类似的证明。使用Weber模型系统所得的结果在特征值参数从势阱底部到有限值的整个范围内是一致的。 显示英文摘要

摘要： 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.