A graphical representation of these partitioned and coupled excitations can be found in Fig. . The amplitudes t α , t n , and t αñ can be solved by projection (Eq. 130). This requires to evaluate ĤPF = e -T ĤPF e T , which is the similarity-transformed Hamiltonian operator, where ĤPF is expressed in Eq. 104 and is usually rotated to the coherent state basis (see Eq. 120). This leads to the ground state energy as a solution to the following set of equations,