Recurrence relation for relativistic atomic matrix elements

Details Recurrence relation for relativistic atomic matrix elements Recurrence relation for relativistic atomic matrix elements

2000-04-26

arxiv.org/abs/quant-ph/0004099v1

Physics

Quantum Physics

10 pages, no figures

Scientific paper

10.1088/0953-4075/33/10/101

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.

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