Quasi-exact solvability of Dirac equation with Lorentz scalar potential

Abstract

We consider exact/quasi-exact solvability of Dirac equation with a Lorentz scalar potential based on factorizability of the equation. Exactly solvable and $sl(2)$-based quasi-exactly solvable potentials are discussed separately in Cartesian coordinates for a pure Lorentz potential depending only on one spatial dimension, and in spherical coordinates in the presence of a Dirac monopole.

arXiv comment10 pages, no figures

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Cited by in corpus (13)

• (1+1)-Dirac particle with position-dependent mass in complexified Lorentz scalar interactions: effectively PT-symmetric
• Relativistic Solutions of Generalized-Dunkl Harmonic and Anharmonic Oscillators
• Transmutations for Darboux transformed operators with applications
• Transmutations and spectral parameter power series in eigenvalue problems
• Prepotential approach to exact and quasi-exact solvabilities
• (Quasi)-exactly solvable quasinormal modes
• Simple unified derivation and solution of Coulomb, Eckart and Rosen-Morse potentials in prepotential approach
• Energy-levels crossing and radial Dirac equation: Supersymmetry and quasi-parity spectral signatures
• Quasi-exactly solvable Fokker-Planck equations
• The use of Slater-type spinor orbitals in algebraic solution of two-center Dirac equation
• Dirac equation with complex potentials
• Shape invariance in prepotential approach to exactly solvable models
• Prepotential approach to quasinormal modes