Solutions of Pauli-Dirac Equation in terms of Laguerre Polynomials within Perturbative Scheme

Abstract

We search for first- and second-order corrections to the energy levels of the Pauli-Dirac equation within the Rayleigh-Schrödinger theory. We use some identities satisfied by the associated Laguerre polynomials to reach this aim. We give a list presenting analytical forms of some integrals including two associated Laguerre polynomials, or their derivatives.

arXiv comment12 pages

References in corpus (7)

• Quasi-exact solvability of Dirac-Pauli equation and generalized Dirac oscillators
• Direct spreading measures of Laguerre polynomials
• The Hahn polynomials in the nonrelativistic and relativistic Coulomb problems
• Bound states of neutral particles in external electric fields
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• First and second-order relativistic corrections to the two and higher-dimensional isotropic harmonic oscillator obeying the spinless Salpeter equation
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Cited by in corpus (1)

• Three-Dimensional Eigenvalues of Harmonic Oscillator- and Coulomb-type Potentials from One-Dimensional Generalized Morse Potential: Perturbative Analyse based on Generalized Laguerre Polynomials