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)

摘要 本文给出了采用新型两步数值方法求解一维薛定谔方程（Schrödinger equation）的详细Mathematica符号推导过程与配套程序。我们通过引入四阶与六阶导数，将传统Numerov方法（Numerov's method）的精度从四阶提升至十二阶，并将周期区间从(0,6)拓展至(0,9.7954)与(9.94792,55.6062)。本程序采用高效算法计算the fir[原文此处截断]。
程序标题：ShdEq.nb
目录编号：ADTT_v1_0
问题本质：针对一维或径向薛定谔方程开展数值积分，以求解束缚态的本征值与连续态的相移。
Mendeley数据集中的CPC程序库版本：
ADTT_v1_0; ShdEq.nb; 10.1016/j.cpc.2004.02.010
本程序源自贝尔法斯特女王大学馆藏的CPC程序库（1969-2018年）