Averaged t-matrix Approximation
⟨ T 0 ⟩ 0 = A = t 0 A [ 1 + G ~ ∑ n ≠ 0 ⟨ T n ⟩ ] = t 0 A ⟨ t 0 ⟩ − 1 ⋅ ⟨ t 0 ⟩ [ 1 + G ~ ∑ n ≠ 0 ⟨ T n ⟩ ] = t 0 ⟨ t 0 ⟩ − 1 ⟨ T 0 ⟩ {\displaystyle {\left\langle T_{0}\right\rangle }_{0=A}=t_{0}^{A}\left[1+{\tilde {G}}\sum _{n\neq 0}\left\langle T_{n}\right\rangle \right]=t_{0}^{A}{\left\langle t_{0}\right\rangle }^{-1}\cdot {\left\langle t_{0}\right\rangle }\left[1+{\tilde {G}}\sum _{n\neq 0}\left\langle T_{n}\right\rangle \right]=t_{0}{\left\langle t_{0}\right\rangle }^{-1}{\left\langle T_{0}\right\rangle }}
から導かれる。この、 ⟨ T 00 ⟩ 0 = A ( B ) {\displaystyle {\left\langle T_{00}\right\rangle }_{0=A(B)}} を、単サイト近似での状態密度の表式に代入すると、