VARIATIONAL APPROACH TO THE DYNAMICS OF ELECTRONS IN METALS

A simple variational method has recently been used to obtain the bulk plasmon dispersion relation. As a variational function a Slater determinant \phi] has been considered, which is related to the Slater determinant \phi0], describing the ground state, by the unitary transformation \phi] = exp ((i/HBAR)S)\phi0], where S is a Hermitian operator of the form S = alpha(t)Q-beta(t)P, with Q = SIGMA(j)cos(q . x(j)), and P=BSIGMA(j)[p(j) . q sin(q . x(j)) + sin(q . x(j))p(j) . q]. The quantum mechanical action principle is used in the harmonic approximation to determine the equations of motion of the collective variables alpha and beta. The method is here extended to the calculation of the dielectric function. The zero point energy of the collective degrees of freedom accounts for most of the correlation energy as obtained by modern techniques