Quasi-exact Solvability of Planar Dirac Electron in Coulomb and Magnetic Fields

Abstract

The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is a physical example of quasi-exactly solvable systems. This model, however, does not belong to the classes based on the algebra $sl(2)$ which underlies most one-dimensional and effectively one-dimensional quasi-exactly solvable systems. In this paper we demonstrate that the quasi-exactly solvable differential equation possesses a hidden $osp(2,2)$ superalgebra.

arXiv commentLaTex, 10 pages, no figures

References in corpus (5)

• Two electrons in an external oscillator potential: hidden algebraic structure
• Quasi-exact solvability of Dirac-Pauli equation and generalized Dirac oscillators
• Charged particles in external fields as physical examples of quasi-exactly solvable models: a unified treatment
• Planar Dirac Electron in Coulomb and Magnetic Fields: a Bethe ansatz approach
• Analytic Solution of a Relativistic Two-dimensional Hydrogen-like Atom in a Constant Magnetic Field

Cited by in corpus (3)

• Prepotential approach to exact and quasi-exact solvabilities
• Simultaneous Ordinary and Type A N-fold Supersymmetries in Schroedinger, Pauli, and Dirac Equations
• Relativistic two-dimensional hydrogen-like atom in a weak magnetic field