Supersymmetric quantum mechanics on non-commutative plane

Abstract 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 ).