Deformed Bound States for Central Fraction Power Potential: Non Relativistic Schrodinger Equation

The Schrodinger equation for central fraction power potential was solved by applying the Boopp's shift method to first order in the non-commutative (NC) parameter theta. It is shown that the deformed NC Hamiltonian represented by a diagonal matrix has two parts. The first part is the usual Hamiltonian, whereas the second part describes the spin-orbit interaction. Furthermore, we show that the Hamiltonian obtained describes modified Zeeman's effect. It was observed that the energy spectra changed radically and replaced by degenerate new states depending on 3- new quantum numbers: j, l and s(z) = +/-1/2 corresponding to the two spin states (up and down) of electron.