It is shown that the lowest random phase approximation (RPA) excitation ene
rgies of a quantum many-fermion system can be obtained by minimizing an eff
ective classical energy functional. The idea is based on an analogy between
the RPA and classical Hamiltonian equations of motion. Generalized Lanczos
recursion allows the minimum to be found very efficiently. The technique i
s used to find the electronic excitation spectrum of the C-60 molecule.