Ebert - Psi-k

Ludwig
Maximilians-
Universität
München
Transition matrix T
The transition or T-matrix T relates by definition
the unperturbed and perturbed systems via
V |Ψ 1 〉 = T |Ψ 0 〉
inserting repeatedly |Ψ 1 〉 = |Ψ 0 〉 + G 0 V |Ψ 1 〉 gives
T = V + V G 0 V + V G 0 V G o V + · · ·
Iterating the Dyson equation the same way one is led to
V G = T G 0
Lippmann-Schwinger equation |Ψ 1 〉 = |Ψ 0 〉 + G 0 T |Ψ 0 〉
Dyson equation G = G 0 + G 0 T G 0
KKR07 – p.14/100