  In this paper we give a proof of the {\it Hecke quantum unique ergodicity
conjecture} for the multidimensional Berry-Hannay model. A model of quantum
mechanics on the 2n-dimensional torus. This result generalizes the proof of the
{\it Rudnick-Kurlberg Conjecture} given in \cite{GH3} for the 2-dimensional
torus.
