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# Accession Number:

## ADA151765

# Title:

## Computer Modeling of Vibrational Energy Levels of Potential Laser Candidates (Diatomic Molecules).

# Descriptive Note:

## Master's thesis,

# Corporate Author:

## AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING

# Report Date:

## 1984-12-01

# Pagination or Media Count:

##
198.0

# Abstract:

## This thesis developed a finite element solution of the Schrodinger wave equation. This technique is used by a computer program to calculate the energy levels and wave functions of a diatomic molecular for a particular potential energy model. The potential energy model is a function of a set of parameters which a non-linear minimization routine varies before solving the wave equation. This is done in an iterative manner until the calculated energy levels agree in a least squares sense with the observed energy levels. Then the transition probabilities Franck-Condon factors between the wave functions are calculated by another program developed for this thesis. Finally, two programs were written to determine the energy levels observed in spectroscopic data. One uses Dunham coefficients and the Dunham equation while the second uses a least square fit to the data directly. The four programs were tested and appear to work correctly. The numeric solutions were compared with the analytic solutions of the single harmonic oscillator. Originator-supplied keywords include Franck-Condon factors, Diatomic molecules, Molecular vibration, Schrodinger equation, and Numerical analysis.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#