27 research outputs found
Expectation Values in Relativistic Coulomb Problems
We evaluate the matrix elements , where O ={1, \beta, i\alpha n
\beta} are the standard Dirac matrix operators and the angular brackets denote
the quantum-mechanical average for the relativistic Coulomb problem, in terms
of the generalized hypergeometric functions_{3}F_{2} 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.Comment: 16 pages, one table, two appendices, no figures; to appear in J.
Phys. B: At. Mol. Opt. Phy