2009/11/30 by Sergei K. Suslov, Sergeĭ K. Suslov
Mathematics · Physics and Astronomy · #Atomic and Molecular Physics #Coulomb #Coulomb wave function #Diagonal #Diagonal matrix #Dirac (video compression format) #Dirac equation #Geometry #Hypergeometric distribution #Hypergeometric function #Mathematical analysis #Mathematical functions and polynomials #Mathematical physics #Mathematics #Matrix (chemical analysis) #Physics #Product (mathematics) #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Recurrence relation #Series (stratigraphy) #math-ph #math.MP
paper · pdf · doi:10.1103/physreva.81.032110
13 pages, no figures
arxiv created 2009/12/01 · openalex publication_date 2010/03/09 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that the diagonal matrix elements \ensuremath⟨Orp\ensuremath⟩, where O=1,\ensuremathβ,i\mathbf\ensuremathαn\ensuremathβ 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.