The Simple Harmonic Oscillator

1996 Lectures are below

September 27, 1995

The Simple Harmonic Oscillator - Introduction

The Simple Harmonic Oscillator - Hilbert Space Operator Method

The Simple Harmonic Oscillator - Boundary Conditions; Matrix Elements

The Simple Harmonic Oscillator - Symmetry; parity A

The Simple Harmonic Oscillator - Symmetry; parity B

The Simple Harmonic Oscillator - Time Dependence; Heisenberg Equation of Motion

The Simple Harmonic Oscillator - Differential Equation Approach

The Simple Harmonic Oscillator - Series Solution

September 29, 1995

The Simple Harmonic Oscillator - Diverging Wave Function and Quantization Condition

The Simple Harmonic Oscillator - Generating Function for Hermite Polynomials and Normalization A

The Simple Harmonic Oscillator - Generating Function for Hermite Polynomials and Normalization B

October 2, 1995

The Simple Harmonic Oscillator Cont. - Two Independent Oscillators and Degeneracy

The Simple Harmonic Oscillator Cont. - Two Coupled Oscillators and Normal Coordinates

The Simple Harmonic Oscillator Cont. - Two Coupled Oscillators; 3D Isotropic Oscillator

The Simple Harmonic Oscillator Cont. - Spherically Symmetric Oscillator and Angular Momentum

Introduction to Matrix Mechanics

Matrix Mechanics Continued

October 6, 1995

Non-Crossing of Energy Levels - Fermi Resonance in CO2 - RAM

Non-Crossing of Energy Levels under a Perturbation

Carbon Dioxide-Normal Modes of Vibration

Infrared Absorptions in Carbon Dioxide-Fermi Resonance

Carbon Dioxide Vibrational States continued

Fermi Resonance - Eigenvalues and Eigenfunctions

October 8, 1996

Lecture 10-8-96: Operator Algebra Approach to the Simple Harmonic Oscillator

October 10, 1996

Lecture 10-10-96: Schrodinger Equation Approach to the Simple Harmonic Oscillator

October 15, 1996

Lecture 10-15-96: SHO: Two Coupled Oscillators-Normal Modes; Three Isotropic Oscillators in Spherical Polar Coordinates

Overheads are below

Overheads: The Simple Harmonic Oscillator

Classical Simple Harmonic Oscillator

Operators

Commutation Relations

Use of Commutator Algebra

Creation and Annhilation Operators

Eigenenergy and Wave Function

Matrix Elements A

Matrix Elements B

Closure Relation

Coordinate Representation of SHO Ket

Coordinate Representation continued

Parity A

Parity B

Parity C

Time Dependence of Creation and Annhilation Operators

Heisenberg Equation of Motion continued

Overheads: Brief Introduction to Matrix Mechanics

Introduction to Matrix Mechanics A

Introduction to Matrix Mechanics B

Introduction to Matrix Mechanics C

Introduction to Matrix Mechanics D

Introduction to Matrix Mechanics E

Introduction to Matrix Mechanics F

Introduction to Matrix Mechanics G

Introduction to Matrix Mechanics H

Introduction to Matrix Mechanics I

Introduction to Matrix Mechanics J

Introduction to Matrix Mechanics K

Introduction to Matrix Mechanics L

Overheads: Vibrational Spectrum of Carbon Dioxide and Fermi Resonance

Introduction to the Vibrational Structure of CO2

Non-Crossing of Perturbed Energy Levels A

Non-Crossing of Perturbed Energy Levels B

Non-Crossing of Perturbed Energy Levels C

Non-Crossing of Perturbed Energy Levels D

Non-Crossing of Perturbed Energy Levels E

Non-Crossing of Perturbed Energy Levels F

Carbon Dioxide Vibrational Energies

Normal Modes of Vibration

Observed Vibrational States of Carbon Dioxide

Normal Modes of Vibration

Fermi Resonance A

Fermi Resonance B

Fermi Resonance C

Fermi Resonance D

Further Discussion of Fermi Resonance

More Discussion of Fermi Resonance

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