  Surface modes are coupled electromagnetic/electrostatic excitations of free
electrons near the vacuum-plasma interface and can be excited on a sufficiently
dense plasma half-space. They propagate along the surface plane and decay in
either sides of the boundary. In such dense plasma models, which are of
interest in electronic signal transmission or in some astrophysical
applications, the dynamics of the electrons is certainly affected by the
quantum effects. Thus, the dispersion relation for the surface wave on a
quantum electron plasma half-space is derived by employing the quantum
hydrodynamical (QHD) and Maxwell-Poison equations. The QHD include quantum
forces involving the Fermi electron temperature and the quantum Bohm potential.
It is found that, at room temperature, the quantum effects are mainly relevant
for the electrostatic surface plasma waves in a dense gold metallic plasma.
