We propose an extended quantum mechanical formalism that is based on a
wave operator <(rho)over cap>, which is related to the ordinary densi
ty matrix via rho = <(rho)over cap><(rho)over cap>(dagger). This forma
lism allows a (generalized) unitary evolution between pure and mixed s
tates. 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.