  We propose an extension of Quantum Mechanics based on the idea that the
underlying "quantum noise" has a non-zero, albeit very small, correlation time
$\tau_c$. The standard (non-relativistic) Schrodinger equation is recovered to
zeroth order in $\tau_c$, and the first correction to energy levels is
computed. Some consequences are discussed, in particular the violation of
Heisenberg's uncertainty principle and the restoration of locality at short
times.
