Unitary Evolution between Pure and Mixed States

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