Eur. Phys. J. B 59, 519-525 (2007)
https://doi.org/10.1140/epjb/e2007-00308-y

Vanishing integral relations and expectation values for Bloch functions in finite domains

Austrian Research Centers GmbH - ARC, Smart Systems Division, Donau-City Straße 1, 1220 Wien, Austria

Corresponding author: ^a christoph.pacher@arcs.ac.at

Received: 28 March 2007
Revised: 21 July 2007
Published online: 15 November 2007

Abstract

Integral identities for particular Bloch functions in finite periodic systems are derived. All following statements are proven for a finite domain consisting of an integer number of unit cells. It is shown that matrix elements of particular Bloch functions with respect to periodic differential operators vanish identically. The real valuedness, the time-independence and a summation property of the expectation values of periodic differential operators applied to superpositions of specific Bloch functions are derived.