FAILURE OF THE HILL DETERMINANT METHOD FOR THE SEXTIC ANHARMONIC-OSCILLATOR

An extended analysis of eigenvalues and wavefunctions resulting from the Hill determinant method is carried out for the one-dimensional sextic anharmonic oscillator. It is shown that, in spite of a seemingly natural ansatz of the method, irrelevant wavefunctions may appear, leading to incorrect eigenvalues. The domain of applicability of the method is limited and its practical use demands a priori investigation before concrete calculations of spectral characteristics. Effective variational calculations based on adequate trial functions are performed and comparison of the results of both approaches is presented.