Some Properties of Exponentially Damped Wave Functions [chapter]

C. A. Mead
1969 Tunneling Phenomena in Solids  
We know from Bloch's theorem that the wave function ψ of an electron in a semiconducting or insulating crystal can be written where k is the wave vector of the state and u(x) is a periodic function with the lattice period of the crystal. Over reasonable distances the u(x) part of the function averages out, and we can view the propagating part e ikx as a quasi-particle behaving in much the same way as a particle in free space. The dynamics of this particle are given by the dispersion relation
more » ... persion relation between the wave vector k and the energy E. For a semiconductor or insulator with a forbidden gap, the dispersion relation is something like the one shown in Fig. 1 . * Re-typeset from original material by Donna Fox (January 2018).
doi:10.1007/978-1-4684-1752-4_9 fatcat:d2avuhsb3rcqtocz7lfnrsutwa