Vanishing Integral Relations and Expectation Values for Bloch Functions in Finite Domains

Details Vanishing Integral Relations and Expectation Values for Bloch Functions in Finite Domains Vanishing Integral Relations and Expectation Values for Bloch Functions in Finite Domains

2007-03-28

arxiv.org/abs/cond-mat/0703734v1

Physics

Condensed Matter

Other Condensed Matter

10 pages

Scientific paper

10.1140/epjb/e2007-00308-y

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.

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