Deciphering the coalescence behavior of Coulomb-Schrödinger atomic wave functions from an operator-product expansion

被引：0

作者：

Huang, Yingsheng ^{[1
,2
,3
]}

Jia, Yu ^{[1
,2
]}

Yu, Rui ^{[1
,2
,4
,5
]}

机构：

[1] Chinese Acad Sci, Inst High Energy Phys, Beijing 100049, Peoples R China

[2] Univ Chinese Acad Sci, Sch Phys, Beijing 100049, Peoples R China

[3] Univ Utah, Dept Phys & Astron, Salt Lake City, UT 84112 USA

[4] Inner Mongolia Univ, Sch Phys Sci & Technol, Hohhot 010021, Peoples R China

[5] Beijing Computat Sci Res Ctr, Beijing 100049, Peoples R China

来源：

PHYSICAL REVIEW A | 2025年 / 111卷 / 03期

基金：

中国国家自然科学基金;

关键词：

EFFECTIVE FIELD-THEORY; SYSTEMS; STATE; QCD;

D O I：

10.1103/PhysRevA.111.032814

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

We revisit the coalescence behavior of the atomic Schr & ouml;dinger wave functions from the angle of an operatorproduct expansion (OPE) within the nonrelativistic Coulomb-Schr & ouml;dinger effective-field theory. We take the electron-nucleus coalescence as an explicit example to demonstrate our formalism, by proving an exact OPE relation to all orders in perturbation theory. As a consequence, the celebrated Kato's cusp condition can be readily reproduced. Our approach can be readily extended to ascertain the multiparticle coalescence behaviors of atomic wave functions, which are otherwise difficult to achieve from the conventional Schr & ouml;dinger equation approach. Moreover, by incorporating relativistic effects, our OPE approach appears to be able to provide key insight for solving a 90-year-old puzzle concerning the peculiar coalescence behavior of the wave function for a Dirac hydrogen atom.

引用

页数：8