Collective modes in metals: quantal and semiclassical approaches

A quantal description (da Providencia Jr and Barberan 1992 Phys. Rev. B 45 6935-7; Barberan and da Providencia Jr 1996 Z. Phys. B 101 3-12) of the collective modes in metals is revisited. Collective variables are explicitly introduced. A time-dependent Slater determinant is assumed for the wavefunction of the system of valence electrons. Analogous models are also investigated using the semiclassical approximation based on the Wigner transform. The results indicate that for those collective modes, which are associated with a large number of particles, namely the cloud of valence electrons, the semiclassical approximation provides good results and is a reliable tool.