Atomic hydrogen in a uniform magnetic field: Low-lying energy levels for fields below109G

The wave function for an electron in combined Coulomb and uniform magnetic fields is expanded in oblatespheroidal angle functions. The resulting Schrödinger equation for the radial function is solved for the energy levels by means of two different adiabatic approximations, which yield rigorous lower and upper bounds on the lowest exact energy levels for each symmetry state of the system. Results are presented for the level and binding energies of hydrogenic $1s$, $2s$, and $2p$ levels for magnetic fields in the range ${10}^7\le B\lesssim {10}^{11}$ G and compared with results of other authors. These results indicate that the present adiabatic approximation methods employing spherical symmetry may be expected to give reliable results for energies of low-lying hydrogenic levels for magnetic fields in the range $0\le B\lesssim {10}^9$ G.