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

Published: 15 June 2004| Version 1 | DOI: 10.17632/tddvdg8gn4.1
Zhongcheng Wang, Yonghua Ge, Yongming Dai, Deyin Zhao


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)



Computational Physics, Computational Method