Energy levels of hydrogen in magnetic fields of arbitrary strength

Abstract

A one-electron wave function is investigated which gives accurate upper bounds on the energy of the ground state and an infinity of excited states of a hydrogenlike atom for arbitrary magnetic-field strengths ranging from zero to asymptotically large values. Qualitative features of the wave function are discussed for different field strengths, and it is noted that a gradual departure from spherical symmetry can be expected as the field strength increases from small values. To deal with this problem, the present wave function combines both spherical and cylindrical symmetry. Results of calculations using this wave function are compared with other existing calculations of the ground-state binding energy of hydrogen, emphasizing the intermediate-field regime. Results for excited states are also examined, and a correspondence is established between the quantum numbers that are appropriate in the two limits of zero and asymptotically large magnetic fields.