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Group theoretical studies of the periodic chart and of configuration mixing in the ground state of helium

Author

Yutaka Kitagawara, University of the Pacific

Date of Award

1977

Document Type

Thesis

Degree Name

Master of Science (M.S.)

Department

Physics

First Advisor

Carl E. Wulfman

First Committee Member

Bruce W. Shore

Second Committee Member

Patrick R. Jones

Third Committee Member

Robert L. Anderson

Abstract

Recently Wulfman found great merit in Barut's idea on atomic super-multiplets, and he introduced the concept of the generalized Hamiltonian that is the Hamiltonian of all atoms. ²⁴ Investigating the Schrodinger equation with this generalized Hamiltonian, it should be possible to relate the properties of different atoms and find the structure of the periodic chart from fundamental principles of dynamics and group theory. One can can use the same kinds of methods for relating the properties of different states of a single hydrogen atom with the aid of the degeneracy group S0 (4) and dynamical group SO (4, 2). These groups represent the symmetries of the time-independent and time-dependent Schrodinger equations with ordinary Hamiltonian.^(25,26) The idea then is to apply these methods to the system defined by a generalized Hamiltonian.

In chapter II of this thesis, we will consider the classification of chemical elements, in the light of the concept of the generalized Hamiltonian. We will make a group theoretical classification based on the characteristics of the outermost electrons in the central-field model of atomic ground states. We conclude that the classification group may be SO (p,q) with p+q≧, p ≧4.

In chapter III of this thesis, we will review Wulfman's work briefly and consider an application of his idea to the ground state of helium making use of the group SO (4,1) xSO (4,1). We arrive at the conclusion that we can obtain physically significant configuration mixing using SO (4,1) xSO (4,1) or SO (4,2) xSO (4,2) in a manner analogous to the way in which SO (4) xSO (4) is used to determine configuration mixing in doubly excited states of helium-like systems.

Pages

88

Recommended Citation

Kitagawara, Yutaka. (1977). Group theoretical studies of the periodic chart and of configuration mixing in the ground state of helium. University of the Pacific, Thesis. https://scholarlycommons.pacific.edu/uop_etds/1954