Abstract
A method is presented whereby matrix elements are derived directly in terms of the eigenenergies and the potential parameters without explicit use of the eigenfunctions. The method consists of determining “initial” matrix elements via quantum mechanical sum rules, and then generating all additional elements through an exact hypervirial recursion relationship. The method is illustrated by sample calculations for the quartic oscillator, and it is shown how one can obtain results more accurate than those computed by direct integration employing numerical eigenfunctions.
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