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.

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