Physical Sciences and Mathematics Commons^™

Group Theoretical Analysis Of In-Shell Interaction In Atoms, Yanfang Ho

University of the Pacific Theses and Dissertations

A group theoretic approach to Layzer's 1/2 expansion method is explored. In part this builds on earlier work of Wulfman(2), of Moshinsky et al(l4), and of Sinanoglu, Herrick(lS), and Kellman (16) on second row atoms.

I investigate atoms with electrons in the 3s-3p-3d shell and find:

1. Wulfman's constant of motion accurately predicts configuration mixing for systems with two to eight electrons in the 3s-3p subshell.

2. The same constant of motion accurately predicts configuration mixing for systems with two electrons in the 3s-3p-3d shell.

3. It accurately predicts configuration mixing in systems of high angular momentum L and of …

Determiningeons : A Computer Program For Approximating Lie Generators Admitted By Dynamical Systems, Gregory G. Nagao

University of the Pacific Theses and Dissertations

As was recognized by same of the most reputable physicists of the world such as Galilee and Einstein, the basic laws of physics must inevitably be founded upon invariance principles. Galilean and special relativity stand as historical landmarks that emphasize this message. It's no wonder that the great developments of modern physics (such as those in elementary particle physics) have been keyed upon this concept.

The modern formulation of classical mechanics (see Abraham and Marsden [1]) is based upon "qualitative" or geometric analysis. This is primarily due to the works of Poincare. Poincare showed the value of such geometric analysis …

The Sl(5r) Lie Invariance Transformation Group For The 3-Dimensional Classical Kepler Problem : A Preparation, And Induced Group Structure Algorithm Derivation, Mark Paul Merner

University of the Pacific Theses and Dissertations

Recently,¹ an algorithm has been derived for the explicit determination of an induced SL (n+2,R) Lie invariance transformation group for a completely integrable 2n - dimensional dynamical system defined on IR²ⁿ from that known for a free particle system with n degree of freedom. ² In particular, the universal transitive Lie invariance transformation group for both the isotropic harmonic oscillator³ and the anharmonic oscillator⁴ (quartic potential) has been obtained by this algorithm. Further,⁵ it has been shown in theory and by example that a complete set of functionally independent constants of motion corresponds to an …

Group Of Point Transformations Of Time Dependent Harmonic Oscillators, Jose Ricardo Bernal

University of the Pacific Theses and Dissertations

In general, a physical system has invariant quantities which are very often related to its symmetry and to the invariance of the equation that describe it. A detailed study of the invariance property of the differential equation will be helpful in understanding this relation.

The work is concerned with a preliminary investigation of the Lie-group which leaves invariant the Newtonian and Lagrangian equation of motion for a one-dimensional harmonic oscillator. A brief review of Ehrenfest's adiabatic principle and the later treatments on exact and adiabatic invariants will be presented.