Abstract

This project aims to provide a numerical solution to the problem of three-dimensional time-independent Schroedinger equation (being spherically symmetrical) by using the Numerov method of number crunching to find the convergence of the energy through the convergence of the wavefunctions hence getting the eigenvalues needed.

But the method provided above needs us to manually input the energy and to find the convergence manually based on a slight difference in the wavefunctions that could be tiresome. Hence another method is used to automatically iterate the trial energy until the eigenvalue is achieved and the method used here is that of the bisection method. The methods utilized above have been used successfully in calculating eigenenergies of the hydrogen and the alkali metals.

The result gotten is then used to find the possible eigenvalues that exist below and above ground state. A software package has been created to allow all these to take place with possible further development.