{"paper":{"title":"The Calculation of Matrix Elements in Relativistic Quantum Mechanics","license":"","headline":"","cross_cats":["physics.chem-ph"],"primary_cat":"physics.atom-ph","authors_text":"A. C. Ilarraza-Lomel\\'i, A. L. Salas-Brito, H. N. N\\'u\\~nez-Y\\'epez, M. N. Vald\\'es-Mart\\'inez, R. P. Mart\\'inez-y-Romero","submitted_at":"2001-09-05T23:42:15Z","abstract_excerpt":"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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"physics/0109015","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}