Accurate computation of the energy spectrum for potentials with multiminima

The eigenvalues of the Schrödinger equation with a polynomial potential are calculated accurately by means of the Rayleigh–Ritz variational method and a basis set of functions satisfying Dirichlet boundary conditions. The method is applied to the well potentials having one, two, and three minima. It is shown, in the entire range of coupling constants, that the basis set of trigonometric functions has the capability of yeilding the energy spectra of unbounded problems without any loss of convergence providing that the boundary value α remains greater than a critical value α cr . Only the computation of the nearly degenerate states of multiwell oscillators requires dealing with a relatively large truncation order.