dorsal/arxiv
View SchemaRelativistically extended Blanchard recurrence relation for hydrogenic matrix elements
| Authors | R. P. Martínez-y-Romero, H. N. Núñez-Yépez, A. L. Salas-Brito |
|---|---|
| Categories | |
| ArXiv ID | physics/0102017 |
| URL | https://arxiv.org/abs/physics/0102017 |
| DOI | 10.1088/0953-4075/34/7/309 |
| Journal | J. Phys. B: At. Mol. Opt. Phys. v. 34 (2001) 1261-1276 |
Abstract
General recurrence relations for arbitrary non-diagonal, radial hydrogenic matrix elements are derived in Dirac relativistic quantum mechanics. Our approach is based on a generalization of the second hypervirial method previously employed in the non-relativistic Schr\"odinger case. A relativistic version of the Pasternack-Sternheimer relation is thence obtained in the diagonal (i.e. total angular momentum and parity the same) case, from such relation an expression for the relativistic virial theorem is deduced. To contribute to the utility of the relations, explicit expressions for the radial matrix elements of functions of the form $r^\lambda$ and $\beta r^\lambda$ ---where $\beta$ is a Dirac matrix--- are presented.
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"abstract": "General recurrence relations for arbitrary non-diagonal, radial hydrogenic\nmatrix elements are derived in Dirac relativistic quantum mechanics. Our\napproach is based on a generalization of the second hypervirial method\npreviously employed in the non-relativistic Schr\\\"odinger case. A relativistic\nversion of the Pasternack-Sternheimer relation is thence obtained in the\ndiagonal (i.e. total angular momentum and parity the same) case, from such\nrelation an expression for the relativistic virial theorem is deduced. To\ncontribute to the utility of the relations, explicit expressions for the radial\nmatrix elements of functions of the form $r^\\lambda$ and $\\beta r^\\lambda$\n---where $\\beta$ is a Dirac matrix--- are presented.",
"arxiv_id": "physics/0102017",
"authors": [
"R. P. Mart\u00ednez-y-Romero",
"H. N. N\u00fa\u00f1ez-Y\u00e9pez",
"A. L. Salas-Brito"
],
"categories": [
"physics.atom-ph"
],
"doi": "10.1088/0953-4075/34/7/309",
"journal_ref": "J. Phys. B: At. Mol. Opt. Phys. v. 34 (2001) 1261-1276",
"title": "Relativistically extended Blanchard recurrence relation for hydrogenic matrix elements",
"url": "https://arxiv.org/abs/physics/0102017"
},
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