  A full viscous quantum hydrodynamic system for particle density, current
density, energy density and electrostatic potential coupled with a Poisson
equation in one dimensional bounded intervals is studied. First, the existence
and uniqueness of a steady-state solution to the quantum hydrodynamic system is
established. Then, utilizing the fact that the third order perturbation term
has an appropriate sign, the local-in-time existence of the solution is
investigated by introducing a fourth order viscous regularization and using the
entropy dissipation method. In the end, the exponential stability of the
steady-state solution is shown by constructing a uniform a-priori estimate.
