Pauli equation on noncommutative plane and the Seiberg–Witten map

Abstract

We study the Pauli equation in noncommutative (NC) two-dimensional plane which exhibits the supersymmetry (SUSY) algebra when the gyro-magnetic ratio is 2. The significance of the Seiberg–Witten (SW) map in this context is discussed and its effect in the problem is incorporated to all orders in [Formula: see text]. We map the NC problem to an equivalent commutative problem by using a set of generalized Bopp-shift transformations containing a scaling parameter. The energy spectrum of the NC Pauli Hamiltonian is obtained and found to be [Formula: see text] corrected which is valid to all orders in [Formula: see text].