TY - JOUR
T1 - Mathematical structure of relativistic Coulomb integrals
AU - Suslov, Sergei
PY - 2010/3/9
Y1 - 2010/3/9
N2 - We show that the diagonal matrix elements Orp, where O={1,β, iαnβ} are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem, may be considered as difference analogs of the radial wave functions. Such structure provides an independent way of obtaining closed forms of these matrix elements by elementary methods of the theory of difference equations without explicit evaluation of the integrals. Three-term recurrence relations for each of these expectation values are derived as a by-product. Transformation formulas for the corresponding generalized hypergeometric series are discussed.
AB - We show that the diagonal matrix elements Orp, where O={1,β, iαnβ} are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem, may be considered as difference analogs of the radial wave functions. Such structure provides an independent way of obtaining closed forms of these matrix elements by elementary methods of the theory of difference equations without explicit evaluation of the integrals. Three-term recurrence relations for each of these expectation values are derived as a by-product. Transformation formulas for the corresponding generalized hypergeometric series are discussed.
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U2 - 10.1103/PhysRevA.81.032110
DO - 10.1103/PhysRevA.81.032110
M3 - Article
AN - SCOPUS:77749304167
SN - 1050-2947
VL - 81
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
IS - 3
M1 - 032110
ER -