Ebert - Psi-k

Ludwig
Maximilians-
Universität
München
Analyticity of the Green’s function
Extension of G + (⃗r, ⃗r ′ , E) to complex energies z
with
(z − H) G(⃗r, ⃗r ′ , z) = δ(⃗r − ⃗r ′ )
ψ i (⃗r)ψ × i (⃗r ′ )
G(⃗r, ⃗r ′ , z) = ∑ i
z − E i
implies G(⃗r, ⃗r ′ , E) to be analytical for Iz ≠ 0 and
G(⃗r, ⃗r ′ , z) = G × (⃗r ′ , ⃗r, z ∗ )
Accordingly one has e.g. for the particle density
n(⃗r) = − 1 ∫ EF
π I dE G + (⃗r, ⃗r, E) = − 1 ∫ EF
π I dz G(⃗r, ⃗r, z)
−
∩
KKR07 – p.10/100