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Research Article

Year : 2018 | Volume: 4 | Issue: 1 | Pages: 4-9

Solution of the Eigenvalue Problems by using Galerkin
Finite Element Method for an External Potential

Azhar Iqbal1*, Jamshaid ul Rahman2

http://dx.doi.org/doi:10.18831/djcivil.org/12018011002

Corresponding author

Azhar Iqbal*

Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University.

  • 1. Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University.

Received on: 2017/01/10

Revised on: 2017/08/28

Accepted on: 2017/10/03

Published on: 2017/10/13

  • Solution of the Eigenvalue Problems by using Galerkin
    Finite Element Method for an External Potential, Azhar Iqbal, Jamshaid ul Rahman, 2017/10/13, Journal of Advances in Civil Engineering, 4(1), 4-9, http://dx.doi.org/doi:10.18831/djcivil.org/12018011002.

    Published on: 2017/10/13

Abstract

A numerical solution of the linear Schrödinger Equation (SE) is found using the Galerkin Finite element method. Test problems were greatly concerned with the external potential which form the core of the paper. First the Schrödinger eigenvalue problem is derived and then it is solved by a finite element method numerically. Finally the numerical results of eigen values and eigen vectors are compared with the exact solutions. The paper starts with a time dependent Schrödinger equation which has a time independent potential.

Keywords

Linear Schrodinger equation, Galerkin finite element method, External potential, Eigen vectors, Eigen values.