Ebert - Psi-k

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Ludwig Maximilians- Universität München Single site Green’s function G ss (⃗r, ⃗r ′ , E) free electrons [E − H 0 ] G 0 (⃗r, ⃗r ′ , E) = δ(⃗r − ⃗r ′ ) single site potential [E − H] G ss (⃗r, ⃗r ′ , E) = δ(⃗r − ⃗r ′ ) j l (r) ↔ j l (r) h + l (r) ↔ h+ l (r) R l (r) ↔ j l (r) − ikh + l (r)t l H l (r) ↔ h + l (r) G 0 (⃗r, ⃗r ′ , E) = −ik ∑ j L (⃗r, E)h +× L (⃗r ′ , E) L G ss (⃗r, ⃗r ′ , E) = −ik ∑ R L (⃗r, E)H × L (⃗r ′ , E) L KKR07 – p.30/100
Ludwig Maximilians- Universität München Alternative Convention for G ss (⃗r, ⃗r ′ , E) boundary conditions at muffin-tin radius r mt G ss (⃗r, ⃗r ′ , E) = −ik ∑ L R L (⃗r, E)H × L (⃗r, E) r→r mt R l −→ Z l = R l t −1 l jl − ikh + l t l replace R L and H L by Z L and J L r→r H mt l −→ h + l G ss (⃗r, ⃗r ′ , E) = ∑ L Z L (⃗r, E)t l (E)Z × L (⃗r, E) − ∑ L Z L (⃗r, E)J × L (⃗r, E) r→r J mt l −→ jl H l = i k ( Zl − J l t −1 ) l r→r Z mt l −→ r→r J mt l −→ jl t −1 l jl − ikh + l Bristol-Oak Ridge convention KKR07 – p.31/100
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