Symmetry in Quantum Mechanics

Prof. J. C. Baird

October 27, 1995

Introduction to Symmetry

Inversion and Permutation Symmetry

Overheads: Symmetry

Introduction to Symmetry: Inversion and the Schrodinger Equation

Introduction to Symmetry: Even and Odd Parity Wave Functions A

Introduction to Symmetry: Even and Odd Parity Wave Functions B

Introduction to Symmetry: Even and Odd Parity Wave Functions C

A 2D Matrix Representation

Multiplication of the 2D Matrix Representations

Formation of the Abstract Group Multiplication Table for the Group of Order Two

October 29, 1995

Inversion as a Transformation in a 2D space: Group Multiplication

Abstract Groups - Group Property

Abstract Groups continued

Abstract Groups continued

Overheads: Abstract Groups

Introduction to Abstract Groups

November 1, 1995

Irreducible Representations. Characters Introduced

Overheads: Representations of Abstract Groups

Representations for the group of order 6 representing the Ammonia Molecule

November 3, 1995

Symmetry in the Ammonia Molecule: A 3D Representations Continued

Symmetry in the Ammonia Molecule

Symmetry in the Ammonia Molecule Continued

Symmetry in the Ammonia Molecule Continued

Symmetry Continued

Overheads: Representations of Abstract Groups

Coordinates for the Ammonia Molecule

3D Representation Matrices for the Ammonia Molecule

Generation of A Four Dimensional Representation for the Ammonia Molecule

A Four Dimensional Representation for the Ammonia Molecule

November 8, 1995

Planer and Bent Formaldehyde: C2v and Cs Symmetry

Planer and Bent Formaldehyde Continued

Bent Formaldehyde Cs

Direct Product Ci x Ci leading to C2v Formaldehyde

Permutation Groups & Young's Tableau

Symmetry Functions and Matrix Element Theorems

Overheads: Symmetry in Ground and Excited States of Formaldehyde

Coordinates for the Ammonia Molecule

November 10, 1995

The Symmetry Function Generation Machine A

The Symmetry Function Generation Machine B

The Matrix Element Theorem. Symmetry Breaking

Formaldehyde: Correlation between Symmetry Groups

Symmetry of Three Coupled Oscillators

Symmetry of Three Coupled Oscillators Continued

Overheads: Symmetry Functions and the Matrix Element Theorem

November 13, 1995

The Rotation Group

The Rotation Group Continued

The Rotation Group: Characters for Two Angular Momenta

The Rotation Group Continued

Summary of Rotation Group Matrix Element Relationships

Overheads: The Pure Rotation Group

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