Exact L2 series solution of the Dirac-Coulomb problem for all energies

被引：18

作者：

Alhaidari, AD ^{[1
]}

机构：

[1] King Fahd Univ Petr & Minerals, Dept Phys, Dhahran 31261, Saudi Arabia

来源：

ANNALS OF PHYSICS | 2004年 / 312卷 / 01期

关键词：

Dirac equation; Coulomb potential; tridiagonal representations; recursion relations; Pollaczek polynomials; scattering; relativistic spectrum;

D O I：

10.1016/j.aop.2004.01.011

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We obtain exact solution of the Dirac equation with the Coulomb potential as an infinite series of square integrable functions. This solution is for all energies, the discrete as well as the continuous. The spinor basis elements are written in terms of the confluent hypergeometric functions and chosen such that the matrix representation of the Dirac Coulomb operator is tridiagonal. The wave equation results in a three-term recursion relation for the expansion coefficients of the wavefunction which is solved in terms of the Meixner-Pollaczek polynomials. (C) 2004 Elsevier Inc. All rights reserved.

引用

页码：144 / 160

页数：17