Circular Rydberg States of the Hydrogen Atom in a Magnetic Field

Dimensional perturbation theory is used to study circular Rydberg states (|m|=n-11) and other large $|m|$ states of the hydrogen atom in a uniform magnetic field. Because of a degeneracy between states of increased angular momentum and states of increased Cartesian dimensionality, the accuracy of the zeroth-order D→∞ limit and a dimensional perturbation expansion improves significantly for states with larger $|m|$. In contrast to other approaches, this method is applicable to the entire range of magnetic field strengths. Energies and expectation values are presented as functions of the field strength.