Criteria of Accuracy of Approximate Wavefunctions

Abstract

The accuracy with which a trial function φ approximates the true wavefunction ψ is quantitatively assessed by the overlap integral S = 〈φ | ψ〉. Upper and lower bounds to S therefore furnish direct criteria of accuracy of the approximation φ and also of the associated physical properties. The available literature on overlap estimates is assembled and critically discussed from a unified point of view, based upon a method of determinantal inequalities. In particular, the relationships among the various approaches are pointed up, several results are extended or generalized, and some new results are obtained. Finally, the various formulas are illustrated by numerical applications to some simple soluble problems.