Mean-Value Point in the Brillouin Zone

A new special point in the Brillouin zone is introduced. It is defined as the point such that the value which any given periodic function of wave vector assumes at this point is an excellent approximation to the average value of the same function throughout the Brillouin zone. This special point is termed the "mean-value point," and is dictated by the crystal symmetry. The coordinates of the mean-value point for cubic lattices are explicitly given.