Supersymmetric Quantum Mechanics on Non-Commutative Plane
arXiv:hep-th/0402064 · doi:10.1016/j.physletb.2004.03.042
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 $B(1+Bθ)$.
11 Pages, references added