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

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

2005-01-09

arxiv.org/abs/quant-ph/0501035v1

Mod. Phys. Lett. A 20 (2005) 673-679.

Physics

Quantum Physics

LaTex, 10 pages, no figures

Scientific paper

10.1142/S0217732305016452

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.

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