Numerical solution of the Schrödinger equations via a reliable algorithm

In this paper, a reliable algorithm for solving Schrodinger equations is established. By second-order central difference scheme, the second-order spatial partial derivative of the Schrodinger 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 Schrodinger equations.

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