Extension and exact realization of the Heller's derivative rule

TL;DR

This paper improves the accuracy of Heller's derivative rule for discretized energy spectra by extending it with additional interpolation points and demonstrates an exact realization method.

Contribution

It introduces Broad's extension to Heller's derivative rule, adding more interpolation points and providing a way to realize the rule exactly without approximation.

Findings

Enhanced accuracy of derivative rule with additional points

Extension scheme enables exact realization of the rule

Applicable to discretized energy spectrum calculations

Abstract

The accuracy of the Heller's derivative rule to calculate the numerical weights associated with discretized energy spectrum is enhanced by Broad's extension which adds (N-1) more interpolating points to the original N points. The extension scheme is then used to show how to realize the rule without any approximation.