Making use of the dielectric permitivitty of a solid state plasma obtained from linearizing a quantum hydrodynamic equation, volume and surface waves in cold semibounded plasma-like media and thin layers of solid state plasmas are investigated in the presence and absence of an external magnetic field. It is shown that quantum oscillation of free charged particles and its spatial dispersion even in cold plasmas lead to new spectra of collective oscillations. Furthermore, a new volume ion-acoustic-type wave is obtained with a quadratic dependence on the wavenumber in the long-wavelength limit. Moreover, it is shown that quantum oscillation affects the surface wave spectrum and extends it to a wider frequency region.