Abstract
A self-consistent tilted-band model is used to generalize the concept of allowed and forbidden bands for a periodic lattice, so as to include the additional effect of an applied electric field. Among the results obtained from this approach are: (1) A previously-proposed tilted-band model has been modified to make it self-consistent, (2) a long-standing controversy over whether the finite-field energy spectrum is adiabatically connected to the zero-field spectrum has been resolved and, (3) it has been shown that the energy eigenfunctions actually relate more to infinite sets of "allowed" and "forbidden" regions in space than to band structures in energy. A new interpretation of the allowed and forbidden bands in crystalline solids is proposed, which is consistent with these results in the zero-field limit.
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