Quasi-exact Solvability of the Pauli Equation

Abstract

We present a general procedure for determining possible (nonuniform) magnetic fields such that the Pauli equation becomes quasi-exactly solvable (QES) with an underlying $sl(2)$ symmetry. This procedure makes full use of the close connection between QES systems and supersymmetry. Of the ten classes of $sl(2)$-based one-dimensional QES systems, we have found that nine classes allow such construction.

LaTex, 20 pages, no figures

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• Shape invariance in prepotential approach to exactly solvable models
• Simultaneous Type A N-fold Supersymmetry with Two Different Values of N
• Simultaneous Ordinary and Type A N-fold Supersymmetries in Schroedinger, Pauli, and Dirac Equations