  The propagation of plasmonic waves in various metallic quantum nanostructures
have considered attention for their applications in technology. The quantum
plasmonic properties of metallic nanostructures in the quantum size regime have
been difficult to describe by an appropriate model. Here the nonlocal quantum
plasmons are investigated in the most important metals of copper, gold, and
silver. Dispersion properties of these metals and propagation of longitudinal
quantum plasmons in the high photon energy regime are studied by a new model of
nonlocal quantum dielectric permittivity. The epsilon near zero properties are
investigated and the spectrum and the damping rate of the longitudinal quantum
plasmons are obtained in these metals. The quantum plasmon s wave function is
shown for both classical and quantum limits. It is shown that silver is the
most appropriate for quantum metallic structures in the development of next
generation of quantum optical and sensing technologies, due to low intrinsic
loss.
