Semiclassical self-consistent-field perturbation theory
for the hydrogen atom in a magnetic field

Alexei V. Sergeev and David Z. Goodson

A recently developed perturbation theory for solving self-consistent-field equations is applied to the hydrogen atom in a strong magnetic field. This system has been extensively studied using other methods and is therefore a good test case for the new method. The perturbation theory yields summable large-order expansions. The accuracy of the self-consistent-field approximation varies according to field strength and quantum state, but is often higher than the accuracy from adiabatic approximations. A new derivation is presented for the asymptotic adiabatic approximation, the most useful of the adiabatic approaches. This derivation uses semiclassical perturbation theory without invoking an adiabatic hypothesis.

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