MATRIX ELEMENTS FOR THE QUARTIC OSCILLATOR

Abstract

A method is presented for the calculation of quartic oscillator matrix elements, $< {n}|{x}^\ell|{n}^{\prime} >$, directly in terms of the eigenenergies, $E_{n}$, without explicit use o£ the eigenfunctions. This method consists of determining ``initial” matrix elements via quantum mechanical sum rules, and then generating all additional elements through an exact hypervirial recursion relation. It will be shown how one can obtain results more accurate than those computed by direct numerical integration employing the eigenfunctions.