Premium
A Self‐Consistent Approach to the Problem of Bloch Electrons in the Electric Field
Author(s) -
Henneberger K.,
Röseler J.
Publication year - 1973
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220580218
Subject(s) - mathematics , bloch wave , equivalence (formal languages) , field (mathematics) , bloch oscillations , mathematical analysis , electron , electric field , set (abstract data type) , physics , quantum mechanics , mathematical physics , pure mathematics , computer science , programming language
Starting from the concept of the “field‐modified model crystal”, a complete set of Bloch functions is self‐consistently defined. The Houston‐type functions constructed with the aid of this set are exact solutions of the time‐dependent Schrödinger equation. The equivalence of the model problem which is defined self‐consistently and the equation given by Wannier is shown. By appropriate choosing the phases of the Bloch functions a splitting of H into two commuting parts is found, the periodic part of which possesses a continuous, but limited spectrum, whereas the Stark‐ladder belongs to the remaining part.