An algebraic method to solve the radial Schrödinger equation

Authors:
M. Gadella;L. P. Lara
Affiliations:
Departamento de Física Teórica, Atómica y Optica, Facultad de Ciencias, 47011, Valladolid, Spain;Departamento de Física, FCEIA, UNR, Av. Pellegrini 250, 2000 Rosario, Argentina and Departamento de Sistemas, FRRO, UTN, Zevallos 1341, 2000 Rosario, Argentina
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

We propose a method of numerical integration of differential equations of the type x^2y^''+f(x)y=0 by approximating its solution with solutions of equations of the type x^2y^''+(ax^2+bx+c)y=0. This approximation is performed by segmentary approximation on an interval. We apply the method to obtain approximate solutions of the radial Schrodinger equation on a given interval and test it for two different potentials. We conclude that our method gives a similar accuracy than the Taylor method of higher order.