Quantum Mechanics with a non-zero quantum correlation time

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.