A large number of higher-energy eigenvalues of a huge dimensional matrix for a quantum chaotic study of a quartic potential

A system of two quartic oscillators coupled by a quartic perturbation is numerically studied for quantum mechanical eigenvalues and classical periodic orbits. The coupling strength serves as a control parameter to simulate the transition from integrable to chaotic regimes. In order to obtain higher-energy eigenvalues of a huge dimensional matrix, the Lanczos method and the equi-energy method are investigated for a practical use.