Two-dimensional noncommutative quantum mechanics with the central potential

Abstract

Quantum mechanics in a noncommutative plane with both space noncommutativity and momentum noncommutativity is considered. For a general two-dimensional central field, we show that the theory can be perturbatively solved for large values of the space noncommutative parameter (theta) when the momentum noncommutative parameter ((theta) over bar) is proportional to (h) over bar (2)/theta. We obtain the expressions for the eigenstates and eigenvalues. We also discuss the more general noncommutative algebra which have the nonvanishing commutator for vertical bar(x) over cap (i), (p) over bar (j)vertical bar for different i, j.