Identification of Molecular Laser Transitions Using the Finite Element Method
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH
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This thesis is a continuation of a previous effort which developed a finite element solution of Schrodingers 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 Einsteins Coefficients. These transitions rates can be obtained by solving Schrodingers 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 Schrodingers 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 Einsteins coefficients, can be computed with the numerical eigenfunctions from two different potential surfaces found in this way.
- Lasers and Masers
- Quantum Theory and Relativity