TY - JOUR
T1 - Expectation values in relativistic Coulomb problems
AU - Suslov, Sergei
N1 - Copyright:
Copyright 2009 Elsevier B.V., All rights reserved.
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=70350674918&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=70350674918&partnerID=8YFLogxK
U2 - 10.1088/0953-4075/42/18/185003
DO - 10.1088/0953-4075/42/18/185003
M3 - Article
AN - SCOPUS:70350674918
VL - 42
JO - Journal of Physics B: Atomic, Molecular and Optical Physics
JF - Journal of Physics B: Atomic, Molecular and Optical Physics
SN - 0953-4075
IS - 18
M1 - 185003
ER -