The Hahn polynomials in the nonrelativistic and relativistic Coulomb problems

The Hahn polynomials in the nonrelativistic and relativistic Coulomb problems

We derive closed formulas for mean values of all powers of r in nonrelativistic and relativistic Coulomb problems in terms of the Hahn and Chebyshev polynomials of a discrete variable. A short review on special functions and solution of the Coulomb problems in quantum mechanics is given.

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of mathematical physics 2008-01, Vol.49 (1), p.012104-012104-51
Hauptverfasser: Suslov, Sergei K., Trey, Benjamin
Format: Artikel
Sprache:eng
Schlagworte:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
DIRAC EQUATION
Exact sciences and technology
Mathematical functions
Mathematical methods in physics
Mathematical problems
MATHEMATICAL SOLUTIONS
Mathematics
Physics
POLYNOMIALS
QUANTUM MECHANICS
Quantum theory
RELATIVISTIC RANGE
SCHROEDINGER EQUATION
Sciences and techniques of general use
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We derive closed formulas for mean values of all powers of r in nonrelativistic and relativistic Coulomb problems in terms of the Hahn and Chebyshev polynomials of a discrete variable. A short review on special functions and solution of the Coulomb problems in quantum mechanics is given.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.2830804