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Manuscript Title: A Fortran program for the numerical integration of the one dimensional Schrodinger equation using exponential and Bessel fitting methods.
Authors: J.R. Cash, A.D. Raptis, T.E. Simos
Program title: PHASE1
Catalogue identifier: ABLM_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 56(1990)391
Programming language: Fortran.
Computer: CYBER - 170.
Operating system: NOS VERSION 2.4.3.
Word size: 60
Keywords: General purpose, Exponential and bessel, Methods fitting, Numerical solution of The schrodinger equation, Error control, Phase shift, Second order, Differential equation, Variable stepsize, Of integration.
Classification: 4.3.

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.

Solution method:
The differential equation is integrated numerically by the method described in Comp. Phys. Commun. 44(1987)95. with the local truncation error being controlled by the method described in Comp. Phys. Commun. 36(1985)113 the numerical solution in the asymptotic region is expressed as a linear combination of spherical Bessel functions.

The subroutine ONDIM is applicable to any linear or nonlinear differential equation of the form : y'' = f(x,y). The restriction of the program to the Lenard Jones potential may be removed by changing the function POTENT.

Unusual features:
The steplengths used in integrating the differential equation numerically are chosen automatically by the program in accordance with a local accuracy criterion, which depends on the number of accurate decimal places required in the calculated phase shift.

Running time:
The test run which accompanies this paper took 2.319 CPUs execution time, in a time - sharing environment, to calculate 18 phase shifts (a separate compilation for each phase shift took a total of 7.719 CPUs time).