Ebert - Psi-k

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Ludwig Maximilians- Universität München Angular momentum expansion of ψ(⃗r, E) Solving the Schrödinger equation using the ansatz [ ] −⃗∇ 2 + V (r) ψ(⃗r, E) = Eψ(⃗r, E) ψ(⃗r, E) = ∑ L R l (r, E)Y L (ˆr) leads to the radial Schrödinger equation [ − ∂2 l(l + 1) + ∂r2 r 2 + V (r) for the radial wave function R l (r, E) ] R l (r, E) = 0 KKR07 – p.24/100
Ludwig Maximilians- Universität München Partial wave decomposition Lippmann-Schwinger equation ∫ ψ(⃗r, E) = e i⃗k⃗r + d 3 r ′ G 0 (⃗r, ⃗r ′ , E) V n (⃗r) ψ(⃗r, E) Ω n ∫ = e i⃗k⃗r + d ∫Ω 3 r ′ d 3 r ′′ G 0 (⃗r, ⃗r ′ , E) t n (⃗r ′ , ⃗r ′′ , E) e i⃗ k⃗r ′′ n Ω n angular momentum expansion R L (⃗r, E)=j L (⃗r, E) ∫ −ik d 3 r ′ h + L (⃗r >, E)j × L (⃗r , E)j × L (⃗r
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Ebert - Psi-k

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