We have performed a numerical calculation of the energy dispersion relation of hybrid magneto-electric states (both propagating and evanescent) in an electron waveguide subjected to a magnetic field. Our results are considerably different from those obtained through the Bohr–Sommerfield quantization condition. We have also calculated the density of the magneto-electric states as a function of energy and the velocity versus energy relationships. Finally, we show how the wavefunctions of these states evolve with increasing magnetic field from particle in a box states to edge states. These results are useful in the analysis of numerous recent magnetotransport experiments performed in electron waveguides.

Temperature-dependent Hall-effect measurements on two Cr-doped GaAs samples show a dominant center at E\-0.324-1.4X 10~4T eV, with respect to the valence-band edge. By comparison with secondary-ion mass spectroscopy measurements of the Cr concentration, and recent E PR measurements of the Cr 2+ , Cr 3+ , and Cr 4+ concentration in several samples, it is shown unambiguously that this energy describes the Cr 4+ -*Cr 3+ transition. This is the first conclusive evidence for a charge-state transition involving Cr 4+ in GaAs.