Quantum well electron dynamics in a parallel magnetic field

A fully quantum mechanical analysis of the role of a parallel magnetic field of arbitrary strength in the electron dynamics of a narrow quantum well is carried out here. We present an explicit analytical closed-form solution for Landau-quantized electrons in skipping states of motion between the narrow well walls effectively involving in-plane translational motion and hybridized with the zero-field lowest subband energy eigenstate. There are many such undamped energy eigenstates corresponding to the many Landau levels, but they are not equally spaced in the quantum well.