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

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