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The Calculation of Matrix Elements in Relativistic Quantum Mechanics | | A. C. Ilarraza-Lomel’{i}
; M. N. Valdés-Mart’{i}nez
; A. L. Salas-Brito
; R. P. Mart’{i}nez-y-Romero
; H. N. Nú~nez-Yépez
; | | Date: |
6 Sep 2001 | | Subject: | Atomic Physics; Chemical Physics | physics.atom-ph physics.chem-ph | | 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 $<2| r^lambda |1 >$ and $<2|eta r^lambda |1>$---where $eta$ 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. | | Source: | arXiv, physics/0109015 | | Services: | Forum | Review | PDF | Favorites | |
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