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理论物理通讯：英文版

Effective Way of Finding Common Eigenvectors of Center-of-Mass Coordinate and Mass-Weighted Relative Momenta of Multi-Partite via IWOP Technique

刘述光, 范洪义

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

我们在场发现多国参加的一条方便途径与连续统变量纠缠了状态，它是并列的 center-of-mass 和团加权的相对 momenta 的普通特徵向量，由分解表示被构造由的完全性关系的通常订的 Gaussian 形式操作符分析特徵向量方程。整个推导在操作员的一个订的产品以内基于集成的技术。

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我们在场发现多国参加的一条方便途径与连续统变量纠缠了状态，它是并列的 center-of-mass 和团加权的相对 momenta 的普通特徵向量，由分解表示被构造由的完全性关系的通常订的 Gaussian 形式操作符分析特徵向量方程。整个推导在操作员的一个订的产品以内基于集成的技术。
We construct 2N operators for a N-particle system, namely one center-of-mass coordinate operator, N-1 relative coordinate operators, one total momentum operator and N-1 mass-weighted relative momentum operators, and give common eigenvectors of N compatible observables [Formula: see text], which are composed of N particles' coordinate [Formula: see text] and momentum [Formula: see text]. By compatible, we mean such observables can be simultaneously determined. Using the technique of integration within an ordered product of operators (IWOP), we prove that the common eigenvectors are complete and orthonormal, and hereby qualified for making up a representation. This new representation can be applied to solving some dynamic problems in quantum mechanics.