Numerical solution for one-dimensional independent of time Schrödinger Equation

In this paper, one of the numerical solution method of one- particle, one dimensional timeindependent Schrodinger equation are presented that allows one to obtain accurate bound state eigen values and functions for an arbitrary potential energy function V(x). For each case, we draw eigen functions versus the related reduced variable for the corresponding energies. The paper ended with a comparison of the result obtained by the numerical solutions with those obtained via the analytical solutions. The agreement between the results obtained by analytical solution method and numerical solution is represents the top Numerov method for numerical solution Schrodinger equation with different potentials energy.