The magnetic moment of an electron between mirrors in a homogeneous magnetic field

The anomaly asub(e) of the electron magnetic moment is calculated for stationary electron states in a homogeneous magnetic field H between two parallel mirrors with distance a between them in order to have a simple model for the apparatus-dependent contribution to the measurement of asub(e) in the Geonium spectroscopy experiment. It turns out that the mirror-dependent contribution to asub(e) depends in a nontrivial manner on both H and a. Especially for such values of H and a that the quotient of the cyclotron frequency of the electron and the lowest eigenfrequency of the photon between the mirrors take values 1, 3, 5..., perturbation theory in the fine structure constant α breaks down and resonances between the cyclotron radiation and the stationary photon states between the mirrors appear