Locality principle in wave mechanics.

This paper proves a locality principle for a wave-mechanical particle governed by the Schrödinger equation. It is shown that rho(r,beta), the Laplace transform of the local density of states n(r,E), depends significantly only on the potential V(r') at points r' near r. The effect of changes of V(r') at distant points r' (|x(i)' - x(i)| > a) on rho(r,beta) decay in a Gaussian fashion with a. This result sheds some light on the locality of physical properties of extended systems and provides general support for various local methods of calculation.