Ebert - Psi-k

Ludwig
Maximilians-
Universität
München
Lippmann-Schwinger equation
H 0 : Hamiltonian for unperturbed reference system
(E − H 0 ) Ψ 0 (⃗r, E) = 0
(E − H 0 ) G 0 (⃗r, ⃗r ′ , E) = δ(⃗r − ⃗r ′ )
G 0 (⃗r, ⃗r ′ , E) solving inhomogeneous equation
Treatment of perturbed system H = H 0 + V (⃗r)
(E − H) Ψ(⃗r, E) = 0
(E − H 0 ) Ψ(⃗r, E) = V (⃗r)Ψ(⃗r, E)
solution supplied by Lippmann-Schwinger equation
∫
Ψ(⃗r, E) = Ψ 0 (⃗r, E) + d 3 r ′ G 0 (⃗r, ⃗r ′ , E) V (⃗r) Ψ(⃗r, E)
KKR07 – p.6/100