A New Approach to the Non Relativistic Schrödinger Equation for an Energy-Depended Potential V(r,E_n,l)=V₀(1+ηE_n,l)r² in both Noncommutative Three Dimensional Spaces and Phases

In present work we study the 3-dimensional non relativistic and noncommutative space-phase Schrödinger equation for modified potential (see formula in paper) depends on energy and quadratic on the relative distance, we have obtained the exact modified bound-states solutions. It has been observed that, the energy spectra in ordinary quantum mechanics was changed, and replaced by degenerate new states, depending on new discreet quantum numbers:n, l, j and s=±1/2 . We show the noncommutative new anisotropic Hamiltonian containing two new important terms, the first new term describe the spin-orbit interaction while the second describes the modified Zeeman effect.