  We propose an extended quantum mechanical formalism that is based on a wave
operator $\vr$, which is related to the ordinary density matrix via
$\rho=\vr\vr^\dagger$. 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.
