This equation contains now the unknowns \( R(k_i,k_j) \) (with dimension \( N\times N \)) and \( R(k_0,k_0) \).

We can turn it into an equation with dimension \( (N+1)\times (N+1) \) with a mesh which contains the original mesh points \( k_j \) for \( j=1,N \) and the point which corresponds to the energy \( k_0 \). Consider the latter as the 'observable' point. The mesh points become then \( k_j \) for \( j=1,n \) and \( k_{N+1}=k_0 \).

With these new mesh points we define the matrix $$ \begin{equation} A_{i,j}=\delta_{i,j}-V(k_i,k_j)u_j, \tag{20} \end{equation} $$