  Boundary dependent corrections to the spin energy eigenvalues of an electron
in a weak magnetic field and confined by a harmonic trapping potential are
investigated. The electromagnetic field is quantized through a normal mode
expansion obeying the Maxwell boundary conditions at the material surface. We
couple the electron to this photon field and a classical magnetic field in the
Dirac equation, to which we apply the unitary Foldy-Wouthuysen transformation
in order to generate a non-relativistic approximation of the Hamiltonian to the
desired order. We obtain the Schr\"odinger eigenstates of an electron subject
to double confinement by a harmonic potential and a classical magnetic field,
and then use these within second-order perturbation theory to calculate the
spin energy shift that is attributable to the surface-modified quantized field.
We find that a pole at the eigenfrequency of a set of generalized Landau
transitions gives dominant oscillatory contributions to the energy shift in the
limit of tight harmonic confinement in a weak magnetic field, which also make
the energy shift preferable to the magnetic moment for a physically meaningful
interpretation.
