Quantum levels and Zeeman splitting for two-dimensional hydrogenic donor states in a magnetic field

We have presented exact solutions for two-dimensional (2D) hydrogenic donor states in a magnetic field and a study of quantum levels and Zeeman bifurcation of 2D donor states in different strength of magnetic field. The quadratic effect of the magnetic field partly lifts the degeneracy of 2D donor states in the pure Coulomb potential and results in an increase of all quantum levels. Then, the first-order term of a magnetic field, i.e., the Zeeman term, completely lifts the degeneracy. At strong magnetic field, the degeneracy of Landau levels is lifted by the Coulomb potential. As the magnetic field decreases, all of the values of the energies decrease linearly until the hybridization between Landau and Coulomb levels occurs. In addition, based on the comparison between energies of 2D and 3D states, we conclude that there are smaller diamagnetic shifts for 2D donor states than those for the corresponding 3D donor states.