Sergei K Suslov 2009 J. Phys. B: At. Mol. Opt. Phys. 42 185003 doi:10.1088/0953-4075/42/18/185003
Expectation values in relativistic Coulomb problems
Sergei K Suslov
Show affiliationsWe evaluate the matrix elements 
Orp
, where 
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.
- PACS
-
03.65.Pm Relativistic wave equations
31.30.J- Relativistic and quantum electrodynamic (QED) effects in atoms, molecules, and ions
- Subjects
- Dates
-
Issue 18 (28 September 2009)
Received 2 July 2009, in final form 3 August 2009
Published 9 September 2009
-
Expectation values in relativistic Coulomb problems
Sergei K Suslov 2009 J. Phys. B: At. Mol. Opt. Phys. 42 185003
-
Experimental and theoretical progress in interaction-free measurements
P G Kwiat 1998 Phys. Scr. 1998 115
-
First joint search for gravitational-wave bursts in LIGO and GEO 600 data
B Abbott et al 2008 Class. Quantum Grav. 25 245008
-
Charge renormalization, effective interactions, and thermodynamics of deionized colloidal suspensions
A R Denton 2008 J. Phys.: Condens. Matter 20 494230
-
Photoionization of C60: a model study
Mohamed E Madjet et al 2008 J. Phys. B: At. Mol. Opt. Phys. 41 105101
-
Photoelectron angular correlation pattern in sequential two-photon double ionization of neon
A S Kheifets 2009 J. Phys. B: At. Mol. Opt. Phys. 42 134016
-
General transformation formulas for Fermi–Walker coordinates
David Klein and Peter Collas 2008 Class. Quantum Grav. 25 145019
-
The remarkable relations among PDEs integrable by the inverse spectral transform method, by the method of characteristics and by the Hopf–Cole transformation
A I Zenchuk and P M Santini 2008 J. Phys. A: Math. Theor. 41 185209
-
Local structure in Ag3[Co(CN)6]: colossal thermal expansion, rigid unit modes and argentophilic interactions
Michael J Conterio et al 2008 J. Phys.: Condens. Matter 20 255225
-
Derivation of a non-local interfacial model for 3D wetting in an external field
N R Bernardino et al 2009 J. Phys.: Condens. Matter 21 465105
Users also read
What's this?- Unified ab initio treatment of attosecond photoionization and Compton scattering
- Variational ansatz for the nonlinear Landau–Zener problem for cold atom association
- Ion momentum spectroscopy of N2 and O2 molecules irradiated by EUV free-electron laser pulses
Related review articles
What's this?- Essential entanglement for atomic and molecular physics
- Dynamical decoherence control of multi-partite systems
- Experimental quantum simulations of many-body physics with trapped ions