Abstract
In Sect. 2.3, we discussed various descriptions of the electronic states of a periodic potential in an electric field. The approximation most frequently used to obtain analytic solutions for the wave functions is the single-band approximation, which neglects the coupling to higher bands. Such descriptions are expected to work well at not too high fields, when the electronic states of the first band in a given well do not come into resonance with the states of the second band in a potential well close by. As discussed above, in the single-band approximation, the wave function would then completely localize in the high-field limit, and transport would be completely suppressed if there were no scattering.
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