多重散乱理論
t n = v n + v n G ~ { v n + v n G ~ v n + v n G ~ v n G ~ v n ⋯ } = v n + v n G ~ t n {\displaystyle t_{n}=v_{n}+v_{n}{\tilde {G}}\{v_{n}+v_{n}{\tilde {G}}v_{n}+v_{n}{\tilde {G}}v_{n}{\tilde {G}}v_{n}\cdots \}=v_{n}+v_{n}{\tilde {G}}t_{n}}
である。総散乱行列TはサイトnでのTnの和、
T = ∑ n T n {\displaystyle T=\,\sum _{n}T_{n}}
と表現でき、各Tnは、
T n = v n + v n G ~ ∑ m v m + v n G ~ ∑ m v m G ~ ∑ p v p + ⋯ = v n { 1 + G ~ [ ∑ m v m + ∑ m v m G ~ ∑ p v p + ⋯ ] } = v n [ 1 + G ~ ∑ m T m ] {\displaystyle {\begin{aligned}T_{n}&=v_{n}+v_{n}{\tilde {G}}\sum _{m}v_{m}+v_{n}{\tilde {G}}\sum _{m}v_{m}{\tilde {G}}\sum _{p}v_{p}+\cdots \\&=v_{n}\left\{1+{\tilde {G}}\left[\sum _{m}v_{m}+\sum _{m}v_{m}{\tilde {G}}\sum _{p}v_{p}+\cdots \right]\right\}\\&=v_{n}\left[1+{\tilde {G}}\sum _{m}T_{m}\right]\end{aligned}}}
更に、