Degree Name

Master of Science (MS)

Semester of Degree Completion


Thesis Director

Giles Henderson


A numerical method and corresponding computer algorithm for solving the one-dimensional radial Schrödinger equation to any desired accuracy is developed. The method uses a finite difference scheme in which an initial trial wavefunction is digitalized over a lattice covering the region of integration. The values of a rough solution are then altered at each lattice point by a simple improvement formula decreasing the value of the variational energy until the desired minimum is reached. The accuracy of these solutions depends only on the grid size. This method is characterized and tested with a harmonic oscillator potential. Practical evaluations and applications are given for the Lennard-Jones 12-6 potential, double minimum potentials for hydrogen-bonded solids, and ab initio potentials of the x2π and A2Σ+ states of the hydroxide radical.