Abstract
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.
| Original language | English (US) |
|---|---|
| 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.
In: Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 42, No. 18, 185003, 2009.Research output: Contribution to journal › Article
}
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 -