  The use of cavities to impact molecular structure and dynamics has become
popular. As cavities, in particular plasmonic nanocavities, are lossy and the
lifetime of their modes can be very short, their lossy nature must be
incorporated into the calculations. The Lindblad master equation is commonly
considered as an appropriate tool to describe this lossy nature. This approach
requires the dynamics of the density operator and is thus substantially more
costly than approaches employing the Schr\"odinger equation for the quantum
wave function when several or many nuclear degrees of freedom are involved. In
this work we compare numerically the Lindblad and Schr\"odinger descriptions
discussed in the literature for a molecular example where the cavity is pumped
by a laser. The laser and cavity properties are varied over a range of
parameters. It is found that the Schr\"odinger description adequately describes
the dynamics of the polaritons and emission signal as long as the laser
intensity is moderate and the pump time is not much longer than the lifetime of
the cavity mode. Otherwise, it is demonstrated that the Schr\"odinger
description gradually fails. We also show that the failure of the Schr\"odinger
description can often be remedied by renormalizing the wave function at every
step of the time propagation. The results are discussed and analyzed.
