Abstract
In this letter I report on the first successful verification of the semiclassical matrix element probability distribution for the Hamiltonian systems between integrability and chaos. As for all the other statistical properties of quantum dynamical systems (e.g. level spacing distribution, phase space localization of eigenstates, etc.) the semiclassical limit was found to converge extremely slowly. So a rather abstract dynamical system was used, namely the standard map on a torus, in order to clearly demonstrate the semiclassical regime.