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.
Full text, pdf-format, 14 pages.
Figures: 1, 2, 3,
4, 5, 6.
Final version, LaTex and and figures, pdf.
Final version, PDF file from the journal.