We propose an extended quantum mechanical formalism that is based on a wave operator $\vr$, which is related to the ordinary density matrix via $��=\vr\vr^\dagger$. This formalism allows a (generalized) unitary evolution between pure and mixed states. It also preserves much of the connection between symmetries and conservation laws. The new formalism is illustrated for the case of a two level system.

13 pages, latex. Revised version. To appear in Phys. Rev. Lett