Quantum ion-acoustic wave oscillations on a quantum plasma half-space

We investigate the dispersion properties of surface quantum ion-acoustic wave oscillations on an electron-ion quantum plasma half-space, taking into account the quantum diffraction effects. We deduce the perturbed electron density by using the linearized quantum fluid model, while the ion density perturbation is obtained by the classical theory. We derive an analytical dispersion relation for the surface waves of the system with low-frequency, by applying the Poisson equation as well as the appropriate boundary conditions. We use the dimensionless parameter H, proportional to quantum tunneling effects and show the system support linear quantum ion-acoustic waves, where in the limit of small H, the classical ion-acoustic waves emerge.