  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.
