M. N. Valdés-Martínez

arXiv2003

Recurrence relations for relativistic two centre matrix elements

Recursion formulae are derived for the calculation of two centre matrix elements of a radial function in relativistic quantum mechanics. The recursions are obtained between not necessarily diagonal radial eigensates using arbitrary radial potentials and any radial functions. The only restriction is that the potentials have to share a common minimum. Among other things, the relations so obtained can help in evaluating relativistic corrections to transition probabilities between atomic Rydberg states.

physics.atom-ph↗

arXiv2001

The Calculation of Matrix Elements in Relativistic Quantum Mechanics

Employing a relativistic version of a hypervirial result, recurrence relations for arbitrary non-diagonal radial hydrogenic matrix elements have recently been obtained in Dirac relativistic quantum mechanics. In this contribution honoring Professor Löwdin, we report on a new relation we have recently discovered between the matrix elements $<2| r^λ|1 >$ and $<2|βr^λ|1>$---where $β$ is a Dirac matrix and the numbers distiguish between different radial eigenstates--- that allow for a simplification and hence for a more convenient way of expressing the recurrence relations. We additionally derive another relation that can be employed for simplifying two center matrix element calculations in relativistic atomic or molecular calculations.

physics.atom-ph↗