Scaling-variational treatment of anharmonic oscillators

Abstract

The scaling-variational method is applied to anharmonic-oscillator models with the Hamiltonian H = p/sup 2/+hx/sup 2/+gx/sup 2k/ to enable the discussion of two important aspects not previously analyzed. First, it is shown that the introduction of a scaling factor which is variationally optimized assures us of the correct dependence of the approximate eigenvalue with g. Second, it is shown that quantities E-bar/sub n/ = are very good approximations to the exact eigenvalues whenever the trial function phi/sub n/ satisfies the quantum virial theorem.