Calculation of Matrix Elements for One-Dimensional Quantum-Mechanical Problems

A simple method proposed by Harris et al. using the techniques of transformation theory for the generation of the matrix elements of one‐dimensional potential functions in a discrete, orthonormal basis is shown to be equivalent to Gaussian quadratures when the basis is constructed of orthogonal polynomials. The basis $\exp \mathrm{(in\theta )}$ on $\mathrm{(-\hspace{0.17em}\pi ,\; \pi )}$ is also discussed.