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Exploratory studies of group theoretic methods in atomic physics

Author

Guang-Hui Xu, University of the Pacific

Date of Award

1989

Document Type

Thesis - Pacific Access Restricted

Degree Name

Master of Science (M.S.)

Department

Physics

First Advisor

Carl E. Wulfman

First Committee Member

Bruce W. Shore

Second Committee Member

Neil Lark

Third Committee Member

Patrick R. James

Abstract

The properties of a physical system are determined by its equation of motion, and every such equation admits one-parameter groups which keep the equation invariant. Thus, for a particular system, if one can find the generator of a one-parameter group which keeps the equation and some further function or functional invariant, then one can change this system into others by changing the parameter, while keeping some properties constant. In this way, one can tell why different systems have some common properties. More importantly, one can use this method to find relationships between the physical properties of different systems.

In the next section, we will illustrate the group theoretic approach by applying it to systems of two coupled oscillators and the hydrogen molecular ion. In section III of this thesis, we will investigate the helium atom system, considering both classical and quantum cases. In the quantum case our attention will be concentrated on the Schrodinger equation in matrix form. We will use a finite set of wavefunctions as our basis. Hence the results obtained will be approximate.

Pages

104

Recommended Citation

Xu, Guang-Hui. (1989). Exploratory studies of group theoretic methods in atomic physics. University of the Pacific, Thesis - Pacific Access Restricted. https://scholarlycommons.pacific.edu/uop_etds/2189