Mathematical structure of relativistic Coulomb integrals

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We show that the diagonal matrix elements Orp, where O={1,β, iαnβ} are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem, may be considered as difference analogs of the radial wave functions. Such structure provides an independent way of obtaining closed forms of these matrix elements by elementary methods of the theory of difference equations without explicit evaluation of the integrals. Three-term recurrence relations for each of these expectation values are derived as a by-product. Transformation formulas for the corresponding generalized hypergeometric series are discussed.

Original languageEnglish (US)
Article number032110
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number3
StatePublished - Mar 9 2010

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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