论文标题
量子机械问题中的散射理论
Scattering Theory in Quantum Mechanical Problems
论文作者
论文摘要
讲座的目的是简要描述两粒子量子系统的散射理论的数学背景。我们讨论了该理论的基本对象：波和散射算子以及相应的散射矩阵，并以schrödinger方程为例进行了说明。我们的目标是提出时间依赖和固定的方法，并描述潜在的数学方法。我们还为三个相互作用的量子粒子提供了散射理论的草图，包括散射通道的渐近完整性的困难问题。除了传统的结果外，我们还讨论了针对远程对相互作用而产生的新散射通道。
The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding scattering matrix and illustrate them on the example of the Schrödinger equation. Our goal is to present time-dependent and stationary approaches and to describe the underlying mathematical methods. We also give a sketch of scattering theory for three interacting quantum particles including a difficult problem of the asymptotic completeness of scattering channels. Along with traditional results, we discuss new scattering channels arising for long-range pair interactions.
