  A cuprate superconductor model based on the analogy with atomic nuclei was
shown by Iachello to have an $su(3)$ structure. The mean-field approximation
Hamiltonian can be written as a linear function of the generators of $su(3)$
algebra. Using algebraic method, we derive the eigenvalues of the reduced
Hamiltonian beyond the subalgebras $u(1)\bigotimes u(2)$ and $so(3)$ of $su(3)$
algebra. In particular, by considering the coherence between s- and d-wave
pairs as perturbation, the effects of coherent term upon the energy spectrum
are investigated.
