numerical solution for one-dimensional independent of time schrödinger equation

in this paper, one of the numerical solution method of one- particle, one dimensional timeindependentschrodinger equation are presented that allows one to obtain accurate bound state eigenvalues and functions for an arbitrary potential energy function v(x).for each case, we draw eigen functions versus the related reduced variable for the correspondingenergies. the paper ended with a comparison of the result obtained by the numerical solutions withthose obtained via the analytical solutions. the agreement between the results obtained by analyticalsolution method and numerical solution is represents the top numerov method for numerical solutionschrodinger equation with different potentials energy.