Date of Award


Document Type


Degree Name

Master of Science


Department of Engineering Physics

First Advisor

Paul H. Ostdiek, PhD


This thesis is a continuation of a previous effort which developed a finite element solution of Schrodinger's Equation. The purpose of this research is to extend this previous work, and develop a chemical laser engineering tool for the identification of transition lines. Identification of laser transitions for a new chemical gain medium requires knowledge of Einstein's Coefficients. These transitions rates can be obtained by solving Schrodinger's Equation for diatomic molecules using the method of finite elements. Experimental vibrational eigenvalues for a given electronic state are used to determine the molecular potential surface which yields the closest numerical result. A non-linear minimization routine is used to hunt for this surface by adjusting parameters of energy functions such as the Harmonic, Morse, Lennard-Jones, and Mie potentials. For each set of new parameters selected by the minimization routine, the method of finite elements is used to solve Schrodinger's Equation. The eigenvalues from these solutions are then compared to the experimental values. Through this iterative process, the best potential surface is isolated. Franck Condon factors, which are proportional to Einstein's coefficients, can be computed with the numerical eigenfunctions from two different potential surfaces found in this way.

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