Quasi-exact Solvability of the Pauli Equation

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.