dorsal/arxiv
View SchemaNew recursion relations of matrix elements of $r^\lambda$ and $\beta r^\lambda$ between relativistic hydrogenic eigenstates
| Authors | R. P. Martínez-y-Romero, H. N. Núñez-Yépez, A. L. Salas-Brito |
|---|---|
| Categories | |
| ArXiv ID | physics/0304049 |
| URL | https://arxiv.org/abs/physics/0304049 |
Abstract
We determine exact recurrence relations which help in the evaluation of matrix elements of powers of the radial coordinate between Dirac relativistic hydrogenic eigenstates. The power $\lambda$ can be any complex number as long as the corresponding term vanishes faster than $r^{-1}$ as $r \to \infty$. These formulas allow determining recursively any matrix element of radial powers --$r^\lambda$ or $\beta r^\lambda$, $\beta$ is a Dirac matrix-- in terms of the two previous consecutive elements. The results are useful in relativistic atomic calculations.
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"date_created": "2026-03-02T18:00:43.130000Z",
"date_modified": "2026-03-02T18:00:43.130000Z",
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"abstract": "We determine exact recurrence relations which help in the evaluation of\nmatrix elements of powers of the radial coordinate between Dirac relativistic\nhydrogenic eigenstates. The power $\\lambda$ can be any complex number as long\nas the corresponding term vanishes faster than $r^{-1}$ as $r \\to \\infty$.\nThese formulas allow determining recursively any matrix element of radial\npowers --$r^\\lambda$ or $\\beta r^\\lambda$, $\\beta$ is a Dirac matrix-- in terms\nof the two previous consecutive elements. The results are useful in\nrelativistic atomic calculations.",
"arxiv_id": "physics/0304049",
"authors": [
"R. P. Mart\u00ednez-y-Romero",
"H. N. N\u00fa\u00f1ez-Y\u00e9pez",
"A. L. Salas-Brito"
],
"categories": [
"physics.atom-ph",
"physics.chem-ph"
],
"title": "New recursion relations of matrix elements of $r^\\lambda$ and $\\beta r^\\lambda$ between relativistic hydrogenic eigenstates",
"url": "https://arxiv.org/abs/physics/0304049"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "a221ea8b-cf0e-4696-996b-8288a10df376",
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"variant": "snapshot-2026-03-01",
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