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The Calculation of Matrix Elements in Relativistic Quantum Mechanics

A. C. Ilarraza-Lomelí·M. N. Valdés-Martínez·A. L. Salas-Brito·R. P. Martínez-y-Romero·H. N. Núñez-Yépez
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Abstract

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.

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A. C. Ilarraza-Lomelí, M. N. Valdés-Martínez, A. L. Salas-Brito, R. P. Martínez-y-Romero, H. N. Núñez-Yépez. 2001-09-05. The Calculation of Matrix Elements in Relativistic Quantum Mechanics. https://arxiv.org/abs/physics/0109015

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