Energy Band Structure and Bloch Functions in the Planar Channeling Model with the Kronig‐Penney Potential

Abstract

AbstractThe motion of a charged particle in a one‐dimensional periodic potential of the Kronig‐Penney type is considered. The energy band structure, Bloch wave functions (BWF) in coordinate and momentum representation are investigated in detail. Two sharply distinguished groups of states, i.e. below‐barrier and above‐barrier, are extracted and the role of both of them in the channeling of positively and negatively charged particles is explained. It is shown that only using a dispersion equation form one is able to obtain information on the symmetry properties of the BWF at the edges of energy bands. An estimate of the corresponding regions of the edge coherence in the Brillouin zone is given. In the above‐barrier case a nontrivial effect is found of parity interchange violation of the BWF at the edges of energy bands, connected with the nullification of the reflection coefficient either from the single barrier or well. An oscillatory behaviour of both allowed and forbidden band widths is revealed. The analytical results for different values of the parameters are illustrated by computer calculations.