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

C. Pacher () and M. Peev

The European Physical Journal B: Condensed Matter and Complex Systems, 2007, vol. 59, issue 4, 519-525

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. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Keywords: 3.65.Fd Algebraic methods; 03.65.Nk Scattering theory; 3.65.Ge Solutions of wave equations: bound states; 73.21.Cd Superlattices (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1140/epjb/e2007-00308-y

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