A Fortran program for the numerical integration of the one-dimensional Schrödinger equation using exponential and Bessel fitting methods

Abstract
An efficient algorithm is described for the accurate numerical integration of the one-dimensional Schrödinger equation. This algorithm uses a high-order, variable step Runge-Kutta like method in the region where the potential term dominates, and an exponential or Bessel fitted method in the asymptotic region. This approach can be used to compute scattering phase shifts in an efficient and reliable manner. A Fortran program which implements this algorithm is provided and some test results are ...

Title of program: PHASE1
Catalogue Id: ABLM_v1_0

Nature of problem
This program solves the single-channel Schrodinger equation for the scattering of an electron by the Lenard Jones potential for a specified energy E and angular momentum L. It also calculates the scattering phase shift. The Lenard-Jones potential is used for demonstration purposes. Any other potential can be used just as easily.

Versions of this program held in the CPC repository in Mendeley Data
ABLM_v1_0; PHASE1; 10.1016/0010-4655(90)90022-S

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

摘要：本文描述了一种高效的算法，用于对一维薛定谔方程进行精确的数值积分。该算法在势能项占主导地位的区域采用了一种高阶、变步长的Runge-Kutta方法，在渐近区域则采用指数或贝塞尔拟合方法。此方法可高效且可靠地计算散射相移。同时提供了一种Fortran程序，用于实现该算法，并附有部分测试结果...

程序标题：PHASE1

目录编号：ABLΜ_v1_0

问题性质：本程序求解单个通道的薛定谔方程，模拟电子在Lenard-Jones势场中的散射，针对特定的能量E和角动量L进行计算，并计算散射相移。Lenard-Jones势用于演示目的，任何其他势场均能以同样简便的方式使用。

Mendeley数据中CPC存储库中保存的此程序版本：ABLΜ_v1_0; PHASE1; 10.1016/0010-4655(90)90022-S

本程序已从贝尔法斯特女王大学（1969-2019）的CPC程序库中导入。