### Abstract

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.

Original language | English (US) |
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Article number | 032110 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 81 |

Issue number | 3 |

DOIs | |

State | Published - Mar 9 2010 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

**Mathematical structure of relativistic Coulomb integrals.** / Suslov, Sergei.

Research output: Contribution to journal › Article

}

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.

UR - http://www.scopus.com/inward/record.url?scp=77749304167&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77749304167&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.81.032110

DO - 10.1103/PhysRevA.81.032110

M3 - Article

VL - 81

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 3

M1 - 032110

ER -