标题： 连续谱和共振谱的精确WKB分析 显示英文标题

标题： On continuum and resonant spectra from exact WKB analysis

摘要： 共振现象是许多量子系统的核心，其中共振态通常由S矩阵的极点奇异性来描述。 在本工作中，我们将复数缩放方法（CSM）和精确WKB分析应用于描述散射问题，同时包含束缚态和共振态。 我们基于精确WKB分析计算连续谱，并推导出倒置罗森-莫尔斯势的S矩阵。 我们重新解释了基于CSM的Aguilar--Balslev--Combes定理；然后讨论了Siegert边界条件的物理意义，并在修改后的希尔伯特空间中严格定义了物理态。 我们的分析连接了散射截面和谱理论，提供了对散射理论及相关公式的深入理解。 显示英文摘要

摘要： Resonance phenomena are central to many quantum systems, where resonant states are typically described by pole singularities of S-matrix. In this work, we apply the complex scaling method (CSM) and exact WKB analysis to describe scattering problems, incorporating both bound and resonant states. We compute continuum spectrum based on the exact WKB analysis and derive the S-matrix for the inverted Rosen--Morse potential. We reinterpret the Aguilar--Balslev--Combes theorem, on which CSM is based; we then discuss the physical significance of the Siegert boundary condition and rigorously define physical states in a modified Hilbert space. Our analysis connects the scattering cross-section and spectral theory, providing insights into the scattering theory and related formulas.