Hydrogen-Like Atom In Noncommutative Quantum Mechanics

In this thesis, we study the relativistic hydrogen-like atom on noncommutative phase space. First of all, we review briefly the noncommutative quantum mechanics, as well as the hydrogen-like atom in relativistic quantum mechanics. Then by using the Bopp shift, we obtain the Hamiltonian of hydrogen-like atom on noncommutative phase space. Fur-thermore we calculate the energy corrections due to the noncommutativity of the phase space by treating the θ and θ modified Hamiltonians as perturbations. As example, we calculate the modifications of energy levels2S1/2,2P1/2and2P3/2and their sublevel spac-ings. We find that space-space noncommutativity split the degenerate energy levels2S1/2and2P1/2into three sublevels, and split the energy level2P3/2into four nondegenerate sublevels. The momentum-momentum noncommutativity shifts the energy levels. Thus the degeneracy of the energy levels2S1/2>2P1/2and2P3/2are completely lifted.We also study the energy levels of the two dimensional hydrogen-like atom in exter-nal magnetic field on noncommutative space. We calculate the θ-modified Hamiltonian and the corresponding energy corrections by using the Bopp shift and the perturbation method. It is shown that the degeneracy of the energy levels is lifted by the space-space noncommutativity and the magnetic field.