Supersymmetric Quantum Mechanics on Non-Commutative Plane

We study the Pauli equation on non-commutative plane. It is shown that the Supersymmetry algebra holds to all orders in the non-commutative parameter $θ$ in case the gyro-magnetic ratio $g$ is 2. Using Seiberg-Witten map, the first order in $θ$ correction to the spectrum is obtained in the case of uniform magnetic field. We find that the eigenstates in the non-commutative case are identical to the commutative case provided the magnetic field $B$ is everywhere replaced by $B(1+Bθ)$.

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