Phase-integral method is applied to study semi-classical limit for the spectral problem related to dynamical system describing quantum mechanical evolution with space-time reflection symmetry. The main goal of the paper is to investigate the relationship between analytic properties of the corresponding potential and the structure of limiting spectral graph. Quantization conditions of Bohr-Sommerfeld type are derived specifying localization of the spectrum for the model problem with a one-parameter family of polynomial potentials treated as deformation of a linear one.

中文翻译：

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半经典极限中的WKB渐近性和谱变形

应用相积分法研究与动力学系统相关的光谱问题的半经典极限，该动力学问题描述了具有时空反射对称性的量子力学演化。本文的主要目的是研究相应电位的分析性质与极限谱图结构之间的关系。推导了Bohr-Sommerfeld类型的量化条件，指定了模型问题的频谱局部性，该问题具有被视为线性变量的变形的多项式势的一参数系列。