An improved version of the perturbation theory has been proposed. Expressions for the wave functions and energies of both degenerate and nondegenerate cases are derived. This method provides a simple way to treat problems involving more than one potential in the Hamiltonian and the case when the perturbations are comparable with or larger than the unperturbed Hamiltonian. We use this method to study the ground state of a hydrogenic atom in a uniform magnetic field of arbitrary strength in which the usual perturbation treatment is limited for most semiconductors to a small range of magnetic field.

• Received 17 December 1986

DOI:https://doi.org/10.1103/PhysRevB.35.9287