The ground-state energy of a hydrogen atom in magnetic fields up to 10 10 G has been calculated accurately by a combination of Rayleigh Schrodinger perturbation theory and a simple variational procedure. The wavefunctions are expressed conveniently in spherical polar coordinates and contain only two variational parameters. A similar calculation for the low-lying excited states is successful only up to much lower fields (about 10 8 G), but can be improved in a straightforward fashion by including higher order perturbation corrections.
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Cohen et al. (1981) studied this question.
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