New exact bound states solutions for (C.F.P.S.) potential in the case of non commutative three dimensional non relativistic quantum mechanics

We obtain here the modified bound-states solutions for central fraction power singular potential (C.F.P.S.) in noncommutative 3-dimensional non relativistic quantum mechanics (NC-3D NRQM). It has been observed that the commutative energy spectra was changed, and replaced degenerate new states, depending on four quantum numbers : j, l and s_z=±1/2 corresponding to the two spins states of electron by (up and down) and the deformed Hamiltonian formed by two new operators : the first describes the spin-orbit interaction , while the second obtained Hamiltonian describes the modified Zeeman effect (containing ordinary Zeeman effect) in addition to the usual commutative Hamiltonian. We showed that the isotropic commutative Hamiltonian H_CFPS will be in non commutative space anisotropic Hamiltonian H_NC-CFPS.

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