Hydrogen atoms in arbitrary magnetic fields. I. Energy levels and wavefunctions

Abstract

The energy values of many low-lying states of the one-electron problem in the presence of a homogeneous magnetic field of arbitrary strength (08 T) are calculated with high numerical accuracy for a sufficiently dense mesh of B. The wavefunctions are expanded either in terms of spherical harmonics (weak and moderate fields) or in terms of Landau states (strong and very strong fields), with r- or z-dependent expansion functions that are determined with the use of an adopted version of the MCHF code of Froese Fischer (1978). At intermediate field strengths up to 24 expansion terms are included. The structural change of the wavefunctions with magnetic field is discussed quantitatively for a few representative states. As an application, the splittings of the components of the Lyman- alpha , beta , and the Balmer- alpha lines of the hydrogen atom are presented (including the effects of the finite proton mass) as continuous functions of the field strength over the whole range of B considered.