Electrons in Crystals in a Finite-Range Electric Field

The problem of an electron in a finite-range constant electric field is treated; energy levels and eigenfunctions are calculated for the "empty crystal" and for a Mathieu-type model crystal. It is shown that the addition of boundary conditions may change the solution drastically. The influence of different boundary conditions on the eigenvalues and eigenfunctions is discussed and it is found that the former are relatively insensitive while the...