Ebert - Psi-k

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Ludwig Maximilians- Universität München Benefits of Green’s function based methods Straightforward application to any type of host/impurity system surfaces or arbitrary layered systems disordered systems using appropriate alloy theory response to an external perturbation response functions/susceptibilities transport (Kubo-Greenwood or Landauer-Büttiker-formalism) spectroscopy many-body problems etc. It’s worth to work with Green’s functions ... ... but how to calculate them ??? KKR07 – p.12/100
Ludwig Maximilians- Universität München Born series Lippmann-Schwinger equation in operator notation with G 0 (⃗r, ⃗r ′ , E) = 〈⃗r|G 0 (E)|⃗r ′ 〉 and the energy argument E omitted in the following |Ψ 1 〉 = |Ψ 0 〉 + G 0 V |Ψ 1 〉 iteration leads to the Born series |Ψ 1 〉 = |Ψ 0 〉 + G 0 V |Ψ 0 〉 + G 0 V G 0 V |Ψ 0 〉 +G 0 V G 0 V G 0 V |Ψ 0 〉 + ... solves Lippmann-Schwinger equation iteratively NB: sometimes used for FP single-site problem KKR07 – p.13/100
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Ebert - Psi-k

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