### Abstract

We evaluate the matrix elements 〈Or^{p}〉, 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 _{3}F_{2}(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.

Original language | English (US) |
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Article number | 185003 |

Journal | Journal of Physics B: Atomic, Molecular and Optical Physics |

Volume | 42 |

Issue number | 18 |

DOIs | |

State | Published - 2009 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Atomic and Molecular Physics, and Optics

### Cite this

**Expectation values in relativistic Coulomb problems.** / Suslov, Sergei.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Expectation values in relativistic Coulomb problems

AU - Suslov, Sergei

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

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 -