Abstract
It is shown that in the presence of a crossed electric and magnetic field the electronic states of a semiconductor in the effective-mass approximation are described by a Hamiltonian containing a non-local potential. In order to preserve the gauge invariance of the two-photon interband transition rate, the interaction Hamiltonian between the electrons and the incident radiation has to be generalized. For GaAs, the transition rate between two particular levels is evaluated in both length and velocity gauges demonstrating the correctness of our approach.
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