Ebert - Psi-k

More documents

Recommendations

Info

Ludwig Maximilians- Universität München Reexpansion of the spherical Bessel functions Starting from e i ⃗k( ⃗R+⃗r) = e i ⃗k ⃗R e i⃗k⃗r and Bauer’s identity e i⃗k⃗r = 4π ∑ i l j L (r, k 2 ) Y L (ˆk) one finds: L j L ( ⃗R + ⃗r, E) = 4π ∑ L ′ L ′′ i l−l′ −l ′′ C LL ′ L ′′ j L ′( ⃗R, E) j L ′′(⃗r, E) with the Gaunt coefficients C LL ′ L ′′ = ∫ dˆr Y L (ˆr) Y L ′(ˆr) Y L ′′(ˆr) KKR07 – p.34/100
Ludwig Maximilians- Universität München Reexpansion of the Hankel functions From − 1 4π e ik |⃗r− ⃗R| ∣ ∣⃗r − ⃗R ∣ = −ik ∑ L the expansion for j l ( ⃗R + ⃗r) one finds j L ( ⃗R, k 2 ) h +× L (⃗r, k2 ) and h + L ( ⃗R + ⃗r, E) = ∑ L ′ G 0LL ′( ⃗R, E) j L (⃗r, E) real-space structural Green’s function matrix or G 0LL ′( ⃗R, E) = 4π ∑ L ′′ i l−l′ −l ′′ C LL ′ L ′′ h+ L ′′ ( ⃗R, E) G nm 0LL ′ (E) = 4π ∑ L ′′ i l−l′ −l ′′ C LL ′ L ′′ h+ L ′′ ( ⃗R m − ⃗R n , E) for ⃗R = ⃗R m − ⃗R n KKR07 – p.35/100
Page 1 and 2: Ludwig Maximilians- Universität M
Page 33: Ludwig Maximilians- Universität M
Page 85 and 86:
Ludwig Maximilians- Universität M
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
show all

Ebert - Psi-k

Create successful ePaper yourself

Delete template?

Save as template?