Sergei K Suslov 2009 J. Phys. B: At. Mol. Opt. Phys. 42 185003 doi:10.1088/0953-4075/42/18/185003
Expectation values in relativistic Coulomb problems
Sergei K Suslov
Show affiliationsWe evaluate the matrix elements 
Orp
, where 
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.
- PACS
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03.65.Pm Relativistic wave equations
31.30.J- Relativistic and quantum electrodynamic (QED) effects in atoms, molecules, and ions
- Subjects
- Dates
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Issue 18 (28 September 2009)
Received 2 July 2009, in final form 3 August 2009
Published 9 September 2009
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Expectation values in relativistic Coulomb problems
Sergei K Suslov 2009 J. Phys. B: At. Mol. Opt. Phys. 42 185003
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