Expectation values in relativistic Coulomb problems

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Abstract

We evaluate the matrix elements 〈Orp〉, where 0 = {1,β,iαnβ}are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem, in terms of generalized hypergeometric functions 3F2(1) for all suitable powers. Their connections with the Chebyshev and Hahn polynomials of a discrete variable are emphasized. As a result, we derive two sets of Pasternack-type matrix identities for these integrals, when p → -p - 1 and p → -p - 3, respectively. Some applications to the theory of hydrogenlike relativistic systems are reviewed.

Original languageEnglish (US)
Article number185003
JournalJournal of Physics B: Atomic, Molecular and Optical Physics
Volume42
Issue number18
DOIs
StatePublished - Nov 9 2009

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ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Condensed Matter Physics

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