Title: Numerical solution of the Schrödinger equations via a reliable algorithm

Authors: Mohammad Heidari; Akbar Hashemi Borzabadi

Addresses: School of Mathematics and Computer Science, Damghan University, Damghan, Iran ' School of Mathematics and Computer Science, Damghan University, Damghan, Iran

Abstract: In this paper, a reliable algorithm for solving Schrödinger equations is established. By second-order central difference scheme, the second-order spatial partial derivative of the Schrödinger equations are reduced to a system of first-order ordinary differential equations, that are solved by an efficient algorithm. The comparison of the numerical solution and the exact solution for some test cases shows that the given algorithm is easy and practical for extracting good approximate solutions of Schrödinger equations.

Keywords: Schrödinger equations; finite difference method; numerical algorithms; approximation; second-order central difference; second-order spatial partial derivative; first-order ODEs; ordinary differential equations.

DOI: 10.1504/IJCSM.2015.072967

International Journal of Computing Science and Mathematics, 2015 Vol.6 No.5, pp.417 - 424

Received: 20 Jun 2014
Accepted: 10 Jun 2015
Published online: 10 Nov 2015 *

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