Rayleigh-Ritz Method, Secular Determinant, and Anharmonic Oscillators

Abstract

The standard Rayleigh-Ritz procedure yielding the successive truncations of the secular determinant is applied to any anharmonic oscillator ($x^{2m}$ and in any finite number of dimensions). In this way we obtain a rigorously convergent as well as numerically very effective approximation procedure for any eigenvalue and eigenvector of the abovementioned Hamiltonians.