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Manuscript Title: Nearly exact calculation of the solution of the radial Schrodinger equation.
Authors: L. Marquez
Program title: YUKAWA/RH**LP D JL 72
Catalogue identifier: AAGN_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 5(1973)379
Programming language: Fortran.
Computer: CDC 6600.
Operating system: SCOPE 3.2.
RAM: 50K words
Word size: 60
Keywords: Nuclear physics, Radial wave function, Yukawa, Nuclear physics, Radial wave function, Yukawa, Screened coulomb, Spherical bessel.
Classification: 4.3, 17.16.

Nature of problem:
There are many problems that one finds in elastic scattering that require the solution of the radial Schroedinger equation. There are also many methods to find this solution. All these methods introduce a certain amount of error in the calculation and this has for consequence, for instance, that certain amount of the irregular solution is mixed to the regular solution. In most applications, this error has no significance. However, we encountered a problem for which we wanted to have an accuracy comparable to the capability of the computer.

Solution method:
The Schrodinger equation is put in a form that eliminates the fast variations for the low values of rho. We begin the solution with the power series of rho. We continue this solution by the Taylor series: One most know or find two quantities characteristic of the computer. The relative error, Epsilon s, with which the computer can register a number in its memory. The lower capacity, Epsilon x, which is the lowest absolute value of a quantity that the computer can handle. These two constants are integrated in the program to control its execution and to make sure that during all the execution, the operators remain within the capability of the computer. Restrictions: The program has been used to compute the wave functions given by the Yukawa or screened Coulomb potential, the Coulomb potential and for no potential, that is the spherical Bessel functions. The value of rho varied from a small fraction to several thousands and the value of l varied from l=0 to several thousands. The program could be modified for any potential provided that such a potential and all its derivatives are continuous.