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It is shown that the 2 X 2 matrix Hamiltonian describing the dynamics of acharged spin 1/2 particle with g-factor 2 moving in an arbitrary, spatiallydependent, magnetic field in two spatial dimensions can be written as theanticommuator of a nilpotent operator and its hermitian conjugate.Consequently, the Hamiltonians for the two different spin projections formpartners of a supersymmetric quantum mechanical system. The resultingsupersymmetry algebra can then be exploited to explicitly construct the exactzero energy ground state wavefunction for the system. Modulo this ground state,the remainder of the eigenstates and eigenvalues of the two partnerHamiltonians form positive energy degenerate pairs. We also construct thespatially asymptotic form of the magnetic field which produces a finitemagnetic flux and associated zero energy normalizable ground statewavefunction.Comment: 10 pages, LaTe

CHARGED SPIN-1/2 PARTICLE IN AN ARBITRARY MAGNETIC FIELD IN TWO SPATIAL DIMENSIONS: A SUPERSYMMETRIC QUANTUM MECHANICAL SYSTEM