Ebert - Psi-k

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Ludwig Maximilians- Universität München Original KKR-method Replace differential Schrödinger equation [ ] −⃗∇ 2 + V (⃗r) ψ ⃗k (⃗r, E) = E ⃗k ψ ⃗k (⃗r, E) by integral Lippmann-Schwinger equation ψ ⃗ k (⃗r, E) = ei ⃗k⃗r + ∫ d 3 r ′ G 0 (⃗r, ⃗r ′ , E) V (⃗r ′ ) ψ ⃗ k (⃗r ′ , E) with free electron Green’s function G 0 (⃗r, ⃗r ′ , E) Korringa, Physica 13 392 (1947); Kohn, Rostoker, PRB 94 1111 (1954) KKR07 – p.4/100
Ludwig Maximilians- Universität München KKR secular equation Ansatz: Ψ j ⃗ k (⃗r, E) = ∑ lm Aj ⃗k lm il R l (r, E) Y lm (ˆr) Application of variational principle ⇒ secular equation [t(E j ⃗k )−1 − G 0 ( ⃗ k, E j ⃗k ) ] A j⃗k = 0 t(E) G 0 ( ⃗ k, E j ⃗ k ) t-matrix structure constants matrix minimal numerical basis set used splitting into potential and geometrical part no standard algebraic eigenvalue problem KKR07 – p.5/100
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