New numerical methods applied to solving the one-dimensional eigenvalue problem

Abstract

Two new numerical methods, the log derivative and the renormalized Numerov, are developed and applied to the calculation of bound‐state solutions of the one‐dimensional Schroedinger equation. They are efficient and stable; no convergence difficulties are encountered with double minimum potentials. A useful interpolation formula for calculating eigenfunctions at nongrid points is also derived. Results of example calculations are presented and discussed.