Quasi-exact solvability of Dirac-Pauli equation and generalized Dirac oscillators

TL;DR

This paper shows that certain neutral Dirac particles in specific electric fields, related to generalized Dirac oscillators, form quasi-exactly solvable systems with solutions depending on $sl(2)$ symmetry, across various coordinate systems.

Contribution

It identifies and analyzes quasi-exact solvability in Dirac-Pauli equations with electric fields, expanding understanding of solvable relativistic quantum systems.

Findings

Identification of electric field configurations with quasi-exact solvability

Explicit solutions for some exactly solvable cases

Analysis across spherical, cylindrical, and Cartesian coordinates

Abstract

We demonstrate that neutral Dirac particles in external electric fields, which are equivalent to generalized Dirac oscillators, are physical examples of quasi-exactly solvable systems. Electric field configurations permitting quasi-exact solvability of the system based on the $sl(2)$ symmetry are discussed separately in spherical, cylindrical, and Cartesian coordinates. Some exactly solvable field configurations are also exhibited.