Zero-Point Energy of the Pullen-Edmonds Hamiltonian

Here we wish to apply the newly developed Generalized Moments Expansion (GMX) to the well-known potential \[ U=\frac{1}{2}\left( x^{2}+y^{2}\right) +\alpha x^{2}y^{2}, \] which is used to model such molecular systems as formamide and \textrm{C}% $_{\mathrm{2}}\mathrm{O}_{\mathrm{3}}$. Our motivation is to investigate the numerical accuracy as well as the viability of the GMX for evaluating ground-state energies of quantum Hamiltonian systems. The zero-point energy of this potential is calculated and results are compared to an analogous Lanczos (tridiagonal) matrix truncation as well as to a Canonical Sequence Method approach.