We investigate the propagation of surface electrostatic oscillations on a quantum plasma half-space, taking into account the quantum effects. We derive the quantum surface wavefrequencies of the system, by means the quantum hydrodynamic theory in conjunction with the Poisson equation and applying the appropriate additional quantum boundary conditions.Numerical results show in the presence of the slow nonlocal variations, plasmon wave energies of the system are significantly modified and plasmonic oscillations with blue-shifted frequencies emerge.
