W1 D1: Math Bits

Introduction to the Course

Introduction to Central Forces

Class Notes OneNote Notebook GCF: Introduction to the Classical Central Force Problem
GCF: Introduction to the Quantum Central Force Problem

Unit: Math Bits (PDEs)

Introduction to the Unit
Learning Outcomes

Unit Learning Outcomes: Partial Differential Equations (Math Bits)

Unit: Math Bits (Power Series Solutions of ODEs)

Introduction to the Unit
Learning Outcomes

Unit Learning Outcomes: Power Series Solutions of ODEs (Math Bits)

W1 D2: Math Bits

Eigenfunction Expansions

Optional, Advanced
GCF: Sturm-Liouville Theory
Video: Introduction to Sturm-Liouville Theory

Properties of Legendre Polynomials

GCF: Legendre Polynomials
GCF: Rodrigues' Formula
Wikipedia article on Legendre Polynomials

W1 D3: Math Bits

Vector Spaces/Inner Products (Review)

Review Vector Spaces
GCF: Vector Spaces
Video: Vector Spaces
Video: Inner Products

HW 01 (w/ Solution)
HW 01 (pdf)

Legendre Polynomial Series

Guessing Legendre Coefficients Expanding a Function in Legendre Polynomials.

GCF: Legendre Polynomial Series
GCF: Guessing and Visualizing a Legendre Polynomial Expansion
GCF: Calculating and Visualizing a Legendre Polynomial Expansion

W1 D4: Math Bits

Separation of Variables
Curvilinear

Separation of Variables - Spherical Harmonics

Video: Separation of Variables for a Particle Confined to a Sphere
GCF: Separation of Variables for the Hydrogen Atom
McIntyre 7.4

Legendre's Associated Equation

GCF: Associated Legendre Functions
McIntyre 7.6.2

Change of Variables (Review)

GCF: Change of Variables
Video: Change of Variables in Legendre's Equation

Series Solutions

GCF: Power Series Solutions: Method/Example

Theorems about Power Series Solutions

GCF: Power Series Solutions: Definitions and Theorems

W1 D5: Math Bits

Series Solutions for Legendre Polynomials

GCF: Series Solutions of Legendre's Equation
McIntyre 7.6.1

HW 02 (w/ Solution)
HW 02 (pdf)

W2 D1

PDEs in Physics

GCF: Important PDEs in Physics
GCF: Classification of PDEs
Video: Classification of PDEs

Separation of Variables
Rectangular (Review)

GCF: Separation of Variables

Particle in a 2-D Quantum Box

QuVis Simulation: 2-D Rectangular Box
QuVis Simulation: 2-D Circular Box

Unit: Classical Mechanics Orbits

W2 D2

Systems of Particles

GCF: Systems of Particles
Taylor Chap. 3 (Optional)

Center of Mass

Survivor Outer Space: A kinesthetic approach to (re)viewing center-of-mass

The Two-Body Problem

Center of Mass-1
Center of Mass-2

GCF: Center of Mass
GCF: Reduced Mass
GCF: Central Forces
Taylor 8.1

Central Force Lagrangians

Reduced Mass

GCF: Reduced Mass
Taylor 8.2

W2 D3

Solutions of the Harmonic Oscillator Equation (Review)

Review from ODEs and Oscillations and Waves:}
Video: Linear ODEs w/ constant coefficients, homogeneous
Video: Linear ODEs w/ constant coefficients, inhomogeneous

HW 03 (w/ Solution)
HW 03 (pdf)

Angular Momentum

Angular Momentum SWBQ Planar Orbit

Conservation of
Classical Angular Momentum

GCF: Angular Momentum

W2 D4

Velocity and Acceleration
in Polar Coordinates

Velocity and Acceleration in Polar Coordinates

GCF: Velocity and Acceleration
GCF: Derivatives of Basis Vectors
Acceleration in Polar Coordinates
Taylor 8.2
Review from PH 335:
Video: Time Derivatives of Polar Basis Vectors

Equations of Motion

GCF: Equations of Motion: \(\vec{F}=\mu\vec{a}\)
Taylor 8.3

Change of Variables

Polar Graphs
Circles, Ellipses, Hyperbolas

Polar Plots SWBQ
Conic Sections

GCF: Graphs in Polar Coordinates

Orbit Shape

GCF: Shape of the Orbit
Taylor 8.5

Energy and Angular Momentum
in Polar Coordinates

Angular Momentum in Polar Coordinates

GCF: Kinetic Energy and Angular Momentum

Spherical/Polar Coordinates
(Review)

Curvilinear Coordinates Introduction Curvilinear Basis Vectors

GCF: Coordinates
Video: Basis Vectors (Review from PH 335/422)

W2 D5

Energy

GCF: Equations of Motion: Harmonic Oscillator
GCF: Equations of Motion: \(E=T+U\)

HW 04 Practice (w/ Solution)
HW 04 Practice (pdf)
HW 04 (w/ Solution)
HW 04 (pdf)

W3 D1

More Effective Potentials

Effective Potentials

Acting Out Effective Potentials Effective Potentials

Taylor 8.4 (Optional)
GCF: Effective Potentials

Inverse Square Forces:
Kepler's First Law

Keplerian Orbits and Effective Potentials

GCF: Effective Potentials w/ Orbits Taylor 8.6-8.7

W3 D2

Kepler's Second Law

Kepler's Second Law Effective Potential Diagrams, version 1 Free Particle Effective Potential

NASA: Orbits and Kepler's Laws

Potentials

Air Hockey

GCF: Equations of Motion: Harmonic Oscillator

Orbits Summary

Introduction to the Unit
Learning Outcomes

Unit Learning Outcomes: Classical Mechanics Orbits

GCF: Introduction to the Classical Central Force Problem

Unit: Quantum Mechanics on the Ring

Introduction to the Unit
Learning Outcomes

Unit Learning Outcomes: Quantum Mechanics on a Ring

GCF: Introduction to the Quantum Central Force Problem

W3 D3

Time Dependence Review

Time Evolution Refresher (Mini-Lecture) Time Evolution of the ISW

HW 05 Practice (w/ Solution)
HW 05 Practice (pdf)
HW 05 (w/ Solution)
HW 05 (pdf)

Introduction to Particle on a Ring

Intro to Particle on a Ring

GCF: Separation of Variables on a Ring

Separating out Center-of-Mass: Quantum

GCF: Reduced Mass
McIntyre 7.1

Eigenstates on a Quantum Ring

GCF: Motion on a Ring
McIntyre 7.5

W3 D4

Normalization of Eigenstates on the Ring

GCF: Normalization of States on a Ring

W3 D5

Probabilities for the Ring from Multiple Representations

Working with Representations on the Ring

GCF: Angular Momentum of the Particle on a Ring
Video: Matrix Representations for a Particle on a Ring
Video: Position Representations for a Particle on a Ring
Video: Degeneracy on the Ring

Time Dependence on a Ring

Time Dependence for a Quantum Particle on a Ring Part 1 Visualization of Quantum Probabilities for a Particle Confined to a Ring

GCF: Time Dependence of Ring States
GCF: Visualization of States on a Ring

Meaning of the Wave Function

Wavefunctions on a Quantum Ring

W4 D1

MEMORIAL DAY
No Class

Unit: Angular Momentum in Quantum Mechanics

Introduction to the Unit
Learning Outcomes

W4 D2

Quantum Ring with Separation of Variables

McIntyre 7.5

Schrödinger's Equation:
Spherical Symmetry

GCF: Schrödinger's Equation in Spherical Coordinates
McIntyre 7.2

Rigid Rotor

GCF: Motion on a Sphere
McIntyre 7.4
McIntyre 7.6
Video: Separation of Variables for the Rigid Rotor

W4 D3

Spherical Harmonics:
Properties

Spherical Harmonics

GCF: Spherical Harmonics
McIntyre 7.6.4

W4 D4

Quantum States of the Rigid Rotor

Quantum Systems Reference Sheet Probabilities for a Quantum Particle on a Unit Sphere in Spherical Harmonic Functions

W4 D5

Spherical Harmonics:
Visualization

Spherical Harmonics on a Balloon

GCF: Visualizing Spherical Harmonics
Video: Description of Spherical Harmonics
McIntyre 7.6.5

Rigid Rotor Probabilities & Degeneracy

Probabilities for a Quantum Particle on a Unit Sphere in Spherical Harmonic Functions

W5 D1

Symmetries, Parity, Degeneracy

Time Dependence

Quantum Particle on a Unit Sphere in Dirac Notation

McIntyre 7.6.3

Unit: Quantum Mechanics of the Hydrogen Atom

Introduction to the Unit
Learning Outcomes

W5 D2

Commutation Relations

Angular Momentum Commutation Relations: Lecture

The Radial Equation

McIntyre 8.1-8.4
GCF: The Radial Equation

W5 D3

Asymptotic Behavior

GCF: Asymptotic Solutions of the Radial Equation

W5 D4

Laguerre Polynomals

GCF: Power Series Solution of the Radial Equation
GCF: General Solution of the Radial Equation

Visualizing Radial Functions

Visualizing Radial Wave Functions

Video: Visualization of Radial Functions

Radial Functions

Radial Functions for a Hydrogenic Atom

Hydrogen Atom Wave Functions

McIntyre 8.5-8.6
GCF: States for the Hydrogen Atom

Calculations on Hydrogen Atom States

Quantum Calculations on the Hydrogen Atom Hydrogen Probabilities in Matrix Notation

Hydrogen Spectra

McIntyre 8.3

Hydrogen Atom Visualization of Probability Densities

Visualization of Quantum Probabilities for the Hydrogen Atom

Video: Interpreting Hydrogen Atom Plots
Visualization of Spherical Harmonics
Visualization of Hydrogen Atom

W5 D5

Review

Classical Orbits Equation Sheet Quantum Ring Equation Sheet Quantum Systems Reference Sheet Spherical Harmonics Radial Functions for a Hydrogenic Atom

McIntyre Appendix F Integrals

Learning outcomes

Unit Learning Outcomes: Partial Differential Equations (Math Bits) Unit Learning Outcomes: Power Series Solutions of ODEs (Math Bits) Unit Learning Outcomes: Classical Mechanics Orbits Unit Learning Outcomes: Quantum Mechanics on a Ring Unit Learning Outcomes: Angular Momentum in Quantum Mechanics Unit Learning Outcomes: Quantum Mechanics of the (Unperturbed) Hydrogen Atom

Final Exam

FINAL EXAM

Topic/Day

Activities

Resources

Homework Due