A non-practical way of solving the eigenvalue problem
At the end we can rewrite our solution of the Schroedinger equation in terms of \( n \) coupled equations for the coefficients \( C_H^P \).
This is a very cumbersome way of solving the equation. However, by using this iterative scheme we can illustrate how we can compute the
various terms in the wave operator or correlation operator \( \hat{C} \). We will later identify the calculation of the various terms \( C_H^P \)
as parts of different many-body approximations to full CI. In particular, we can relate this non-linear scheme with Coupled Cluster theory and
many-body perturbation theory.