  The Liouville-von Neumann equation describes the change in the density matrix
with time. Interestingly, this equation was recently regarded as a wave
equation for wave functions but not a equation for density functions. This
setting leads to an extended form of the Schr\"odinger wave equation governing
the motion of a quantum particle. In this paper we obtain the integrability of
the wave propagator arising from the Liouville-von Neumann equation in this
setting.
