dorsal/arxiv
View SchemaThe Calculation of Matrix Elements in Relativistic Quantum Mechanics
| Authors | A. C. Ilarraza-Lomelí, M. N. Valdés-Martínez, A. L. Salas-Brito, R. P. Martínez-y-Romero, H. N. Núñez-Yépez |
|---|---|
| Categories | |
| ArXiv ID | physics/0109015 |
| URL | https://arxiv.org/abs/physics/0109015 |
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 L\"owdin, we report on a new relation we have recently discovered between the matrix elements $<2| r^\lambda |1 >$ and $<2|\beta r^\lambda |1>$---where $\beta$ 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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"abstract": "Employing a relativistic version of a hypervirial result, recurrence\nrelations for arbitrary non-diagonal radial hydrogenic matrix elements have\nrecently been obtained in Dirac relativistic quantum mechanics. In this\ncontribution honoring Professor L\\\"owdin, we report on a new relation we have\nrecently discovered between the matrix elements $\u003c2| r^\\lambda |1 \u003e$ and\n$\u003c2|\\beta r^\\lambda |1\u003e$---where $\\beta$ is a Dirac matrix and the numbers\ndistiguish between different radial eigenstates--- that allow for a\nsimplification and hence for a more convenient way of expressing the recurrence\nrelations. We additionally derive another relation that can be employed for\nsimplifying two center matrix element calculations in relativistic atomic or\nmolecular calculations.",
"arxiv_id": "physics/0109015",
"authors": [
"A. C. Ilarraza-Lomel\u00ed",
"M. N. Vald\u00e9s-Mart\u00ednez",
"A. L. Salas-Brito",
"R. P. Mart\u00ednez-y-Romero",
"H. N. N\u00fa\u00f1ez-Y\u00e9pez"
],
"categories": [
"physics.atom-ph",
"physics.chem-ph"
],
"title": "The Calculation of Matrix Elements in Relativistic Quantum Mechanics",
"url": "https://arxiv.org/abs/physics/0109015"
},
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