Recurrence relation for relativistic atomic matrix elements
Quantum Physics
2009-11-06 v1 Mathematical Physics
math.MP
Atomic Physics
Abstract
Recurrence formulae for arbitrary hydrogenic radial matrix elements are obtained in the Dirac form of relativistic quantum mechanics. Our approach is inspired on the relativistic extension of the second hypervirial method that has been succesfully employed to deduce an analogous relationship in non relativistic quantum mechanics. We obtain first the relativistic extension of the second hypervirial and then the relativistic recurrence relation. Furthermore, we use such relation to deduce relativistic versions of the Pasternack-Sternheimer rule and of the virial theorem.
Cite
@article{arxiv.quant-ph/0004099,
title = {Recurrence relation for relativistic atomic matrix elements},
author = {R P Martínez-y-Romero and H N Núñez-Yépez and A L Salas-Brito},
journal= {arXiv preprint arXiv:quant-ph/0004099},
year = {2009}
}
Comments
10 pages, no figures