Spectrum of Schrodinger Equation with H.L.C. Potential in Non-commutative Two-dimensional Real Space

This paper describes the Schrodinger equation for Harmonic-Linear and Colombian H.L.C. potential that was solved by applying the Boopp's shift method to first order in the non-commutativity parameter theta in non-commutative two-dimensional spaces. The modified energy levels at the fundamental state and first excited states are obtained by applying perturbation theory. The non-commutative Hamiltonian is constructed and the new spectrum was obtained which was produced from two modes of interactions: the first one is the effect of an external magnetic field while the second is spin-orbital interaction. The degenerated states are determined for a given orbital quantum number l.