Summarizing FCI and bringing in approximative methods
If we can diagonalize large matrices, FCI is the method of choice since:
- It gives all eigenvalues, ground state and excited states
- The eigenvectors are obtained directly from the coefficients \( C_H^P \) which result from the diagonalization
- We can compute easily expectation values of other operators, as well as transition probabilities
- Correlations are easy to understand in terms of contributions to a given operator beyond the Hartree-Fock contribution. This is the standard approach in many-body theory.