Green's function for electrons in a narrow quantum well in a parallel magnetic field

Electron dynamics in a narrow quantum well in a parallel magnetic field of arbitrary strength are examined here. We derive an explicit analytical closed-form solution for the Green's function of Landau-quantized electrons in skipping states of motion between the narrow well walls coupled with in-plane translational motion and hybridized with the zero-field lowest subband energy eigenstate. Such Landau-quantized modes are not uniformly spaced.