# Expectation Values in Relativistic Coulomb Problems - Quantum Physics

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Abstract: We evaluate the matrix elements , where O ={1, \beta, i\alpha n\beta} are the standard Dirac matrix operators and the angular brackets denotethe quantum-mechanical average for the relativistic Coulomb problem, in termsof the generalized hypergeometric functions {3}F {2} for all suitable powers.Their connections with the Chebyshev and Hahn polynomials of a discretevariable are emphasized. As a result, we derive two sets of Pasternack-typematrix identities for these integrals, when p->-p-1 and p->-p-3, respectively.Some applications to the theory of hydrogenlike relativistic systems arereviewed.

Autor: Sergei K. Suslov

Fuente: https://arxiv.org/

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