We consider an electron in a 1D random adiabatically changing potentia
l. We demonstrate that the positions of the maxima of an electron eige
nstate probability density do not move even when the change of the pot
ential is significant. We show that at the same time the main maximum
hops by a distance of the order of the size of the system. We present
arguments that such hopping of electron localization position happens
also in two and three dimensions.