Degree Name
Master of Science (MS)
Semester of Degree Completion
1980
Thesis Director
Giles Henderson
Abstract
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.
Recommended Citation
Ko, Chun-Sheng, "A Numerical Method for the Solution of the Schrödinger Equation by a Trial Wavefunction Improvement Formula" (1980). Masters Theses. 3052.
https://thekeep.eiu.edu/theses/3052
Included in
Numerical Analysis and Computation Commons, Partial Differential Equations Commons, Physical Chemistry Commons
