Theoretical Condensed Matter Physics
PD A. Komnik, Universit¨at Heidelberg, SS07 3. Set of Exercises: 15.05.07
5. Free electron gas:
Consider 3D free non-interacting electron gas with density n0. Using the relation between n0 and the Green’s function [eq. (143) of the lecture notes] calculate the Fermi momentum pF of the system,
pF = (3π2n0)1/3.
6. Friedel oscillations:
a) Calculate the Green’s function of 1D free fermions in the energy–coordinate rep- resentation, Gαβ(;x, x0), α, β are the spin indices, denotes the energy and x, x0 are the coordinates.
b) How doesGαβ(;x, x0) change if the system is half-infinite (x >0) with a boundary condition ψ|x=0 = 0 (hard wall potential)?
c) Show that under the conditions of b) the electron density oscillates as a function of x. Evaluate the oscillation period.
