Highorder Kspace linear response of a noninteracting Fermion system in an external potential

The onebody density matrix of a noninteracting Fermion system is expressed in terms of a contour integral, and expanded about that of the free particle system. Highorder kspace linear response functions of this in an external potential are calculated for one and three dimensions via a functional expansion formulation. The results are compared with those given by the inverse Laplace transform (ILT) method. It is shown that the kspace linear responses in one dimension have a much simpler structure than those in the real space, and can be evaluated systematically. Two special onebody Hamiltonians are used to illustrate the onedimensional results. The validity of the linear response expansion is addressed in the discussion of these examples.