Semiclassical Self-consistent--eld Perturbation Theory for the Hydrogen Atom in a Magnetic Eld

A recently developed perturbation theory for solving self-consistent-eld equations is applied to the hydrogen atom in a strong magnetic eld. 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-eld approximation varies according to eld 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.