New Numerov-type methods for computing eigenvalues, resonances, and phase shifts of the radial Schr�dinger equation

Abstract

A new family of P‐stable two‐step Numerov‐type methods with minimal phase lag are developed for the numerical integration of the eigenvalue‐resonance and phase shift problem of the one‐dimensional Schrödinger equation. A new embedding technique to control the phase‐lag error is introduced. Application to various potentials indicates that these new methods are generally more accurate than other previously developed finite‐difference methods. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 467–475, 1997

Phase-space propagation and stability analysis of the 1-dimensional Schrödinger equation for finding bound and resonance states of rotationally excited H2

“…In this representation a second order ODE is replaced by a set of 2 first order ODEs with the Cauchy BCs instead of the Dirichlet BCs of the origi- * caarango@icesi.edu.co nal problem. Numerically this idea is implemented in Numerov's method to obtain both bound and resonance states [23][24][25][26][27][28].…”