  The (group and spin space) matrix Hamiltonian describing the dynamics of a
nonrelativistic spin 1/2 particle moving in a static, but spatially dependent,
non-Abelian magnetic field in two spatial dimensions is shown to take the form
of an anticommutator of a nilpotent operator and its hermitian conjugate.
Consequently, the (group space) matrix Hamiltonians for the two different spin
projections form partners of a supersymmetric quantum mechanical system. The
resulting supersymmetry algebra is exploited to explicitly construct the exact
zero energy ground state wavefunction(s) for the system. The remaining
eigenstates and eigenvalues of the two partner Hamiltonians form positive
energy degenerate pairs.
