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 language | English (US) |
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Article number | 185003 |
Journal | Journal of Physics B: Atomic, Molecular and Optical Physics |
Volume | 42 |
Issue number | 18 |
DOIs | |
State | Published - 2009 |
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
- Condensed Matter Physics