Recurrence relation for relativistic atomic matrix elements

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.

10 pages, no figures

References in corpus (3)

• New non-unitary representations in a Dirac hydrogen atom
• Non-unitary representations of the SU(2) algebra in the Dirac equation with a Coulomb potential
• A new approach to perturbation theory for a Dirac particle in a central field

Cited by in corpus (3)

• Relativistically extended Blanchard recurrence relation for hydrogenic matrix elements
• A useful form of the recurrence relation between relativistic atomic matrix elements of radial powers
• Expression of relativistic expectation values of powers of $r$ in terms of Clebsch-Gordan coefficients