Overlap integral of continuum stationary states

IF 3 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Annals of Physics Pub Date : 2024-07-31 DOI:10.1016/j.aop.2024.169750

Kenzo Ishikawa , Yuya Nishio

引用次数: 0

Abstract

The rigorous formula of overlap integrals of continuum stationary states with their asymptotic expressions in potentials of finite widths are derived. Those of energies $E_{1}$ and $E_{2}$ consist of diagonal terms that are proportional to $δ (E_{1} - E_{2})$ and nondiagonal terms. Owing to the composition of nondiagonal terms, superpositions of stationary states have time-dependent norms and finite probability currents. These do not represent isolate states. In various exceptional potentials and in free theory, nondiagonal terms do not exist, and the superpositions of states with different energies represent isolate particles that exactly describe scattering processes.

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连续静止态的重叠积分

推导了连续静止态重叠积分的严格公式及其在有限宽度势中的渐近表达式。能量和的重叠积分由对角项和非对角项组成，对角项与非对角项成正比。由于非对角项的构成，静止态的叠加具有随时间变化的规范和有限的概率电流。这些并不代表孤立状态。在各种例外势和自由理论中，非对角项并不存在，不同能量状态的叠加代表了精确描述散射过程的孤立粒子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Physics 物理-物理：综合

CiteScore

5.30

自引率

3.30%

发文量

211

审稿时长

47 days

期刊介绍： Annals of Physics presents original work in all areas of basic theoretic physics research. Ideas are developed and fully explored, and thorough treatment is given to first principles and ultimate applications. Annals of Physics emphasizes clarity and intelligibility in the articles it publishes, thus making them as accessible as possible. Readers familiar with recent developments in the field are provided with sufficient detail and background to follow the arguments and understand their significance. The Editors of the journal cover all fields of theoretical physics. Articles published in the journal are typically longer than 20 pages.