The European Physical Journal B

, Volume 59, Issue 4, pp 519–525 | Cite as

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

  • C. PacherEmail author
  • M. Peev
Mathematical Structures in Statistical and Condensed Matter Physics


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.


3.65.Fd Algebraic methods 03.65.Nk Scattering theory 3.65.Ge Solutions of wave equations: bound states 73.21.Cd Superlattices 


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Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.Austrian Research Centers GmbH - ARC, Smart Systems DivisionWienAustria

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