Non-commutative Geometry and Applications to Physical Systems

We obtain exact solutions of the 2D Schrodinger equation with the central potentials V(r) = ar(2) + br(-2) + cr(-4) and V(r) = ar(-1) + br(-2) in a non-commutative space up to the first order of noncommutativity parameter using the power-series expansion method similar to the 2D Schrodinger equation with the singular even-power and inverse-power potentials, respectively, in commutative space. We derive the exact non-commutative energy levels and show that the energy is shifted to m levels, as in the Zeeman effect.