Two-Dimensional Pauli Equation in Noncommutative Phase-Space

In this paper, we investigated the Pauli equation in a two-dimensional noncommutative phase-space by considering constant magnetic field perpendicular to plane. We mapped problem equivalent commutative one through set of Bopp-shift transformation. The energy spectrum and wave function are found, where question has been Landau problem. Further, within classical limit, have derived semi-classical partition system one-particle N-particle systems. Consequently, studied its thermodynamic properties, i.e. Helmholtz free energy, mean specific heat entropy phase-spaces. impact noncommutativity on is successfully examined.