A Mathematica program for the two-step twelfth-order method with multi-derivative for the numerical solution of a one-dimensional Schrödinger equation

Abstract
In this paper, we present the detailed Mathematica symbolic derivation and the program which is used to integrate a one-dimensional Schrödinger equation by a new two-step numerical method. We add the fourth- and sixth-order derivatives to raise the precision of the traditional Numerov's method from fourth order to twelfth order, and to expand the interval of periodicity from (0,6) to the one of (0,9.7954) and (9.94792,55.6062). In the program we use an efficient algorithm to calculate the fir...

Title of program: ShdEq.nb
Catalogue Id: ADTT_v1_0

Nature of problem
Numerical integration of one-dimensional or radial Schrödinger equation to find the eigenvalues for a bound states and phase shift for a continuum state.

Versions of this program held in the CPC repository in Mendeley Data
ADTT_v1_0; ShdEq.nb; 10.1016/j.cpc.2004.02.010

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)