论文标题
散射理论简介
An Introduction to Scattering Theory
论文作者
论文摘要
这些讲座的目的是在一个维度中对量子散射理论进行访问和自我包含的介绍。 A部分定义了理论操场，并在时域（渐近条件，内在和外部，散射操作员$ \ hat {s} $）中开发了散射理论的基本概念。然后，B部分的目的是以分步的方式建立，这是能量领域中时间独立的散射理论。这是为固定散射状态引入lippmann-schwinger方程（称为$ |ψ_{e（\ pm 1）}^\ pm \ rangle $），以讨论$ |的基本属性。 ψ_{e（\ pm 1）}^\ pm \ rangle $，然后以$ |的方式构造$ \ hat {s} $和$ \ hat {t} $ operator ψ_{e（\ pm 1）}^\ pm \ rangle $。然后，通过推导显式公式来照亮$ \ hat {s} $和$ \ hat {t} $ operator的物理内容，以通过推导明确的公式，以通过电位的交互区域/来自电位的交互区域传输/反射我们的量子粒子。给出了一个说明性的数值示例，还突出了散射共振的存在。最后，C部分详细阐述了非赫米特散射理论（Siegert pseudostate形式主义），该理论提供了一种非常强大的工具，适合清晰地了解共鸣现象。
The purpose of these lectures is to give an accessible and self contained introduction to quantum scattering theory in one dimension. Part A defines the theoretical playground, and develops basic concepts of scattering theory in the time domain (Asymptotic Condition, in- and out- states, scattering operator $\hat{S}$). The aim of Part B is then to build up, in a step-by-step fashion, the time independent scattering theory in energy domain. This amounts to introduce the Lippmann-Schwinger equation for the stationary scattering states (denoted as $| ψ_{E(\pm 1)}^\pm \rangle$), to discuss fundamental properties of $| ψ_{E(\pm 1)}^\pm \rangle$, and subsequently to construct $\hat{S}$ and $\hat{T}$ operators in terms of $| ψ_{E(\pm 1)}^\pm \rangle$. Physical contents of the $\hat{S}$ and $\hat{T}$ operators is then illuminated by deriving explicit formulas for the probability of transmission/reflection of our quantum particle through/from the interaction region of the potential. An illustrative numerical example is given, which also highlights an existence of scattering resonances. Finally, Part C elaborates the nonhermitian scattering theory (Siegert pseudostate formalism), which offers an extremely powerful tool suitable for clear cut understanding of the resonance phenomena.
