The quadratic Zeeman effect for weak fields on hydrogen

Using classical mechanics the author analyses the effect of a magnetic field on a hydrogen atom. The field is assumed weak enough for both classical and quantal degenerate perturbation theory to be valid. An approximate Hamiltonian describing the mean motion is found and is shown to have several unusual features. In particular it has a double minimum with phase space comprising regions of both rotational and librational motion. This double minimum produces a degeneracy in the lower levels of the quantal spectrum for sufficiently large principal quantum number. A comparison between the predictions of the classical model, presented here, and purely quantal calculations is made and agreement obtained.