Spring 2022 Central Forces

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01 M 5/2

Introduction

Center of Mass

Systems of Particles
Taylor Chap. 3
Taylor 8.3, first part

02 T 5/3

The Two-Body Problem
Taylor 8.1

Reduced Mass
Taylor 8.2

Spherical/Polar Coordinates
(Review)
Review from 335:
Video: Basis Vectors

Velocity and Acceleration
(Review)
Taylor 8.2
Review from 335:
Video: Time Derivatives of Polar Basis Vectors

03 W 5/4

Polar Graphs
Circles, Ellipses, Hyperbolas
Applet: Orbit Shapes



04 Th 5/5

Conservation of
Classical Angular Momentum

Equations of Motion: F=ma
Taylor 8.3, second part

Change of Variables

Orbit Shape
Taylor 8.5
Review Mth 256:
Video: Linear ODEs w/ constant coefficients, homogeneous
Video: Linear ODEs w/ constant coefficients, inhomogeneous

Orbits for Inverse Square Forces
Taylor 8.6-8.7

05 F 5/6

Potentials

Equations of Motion: E=T+U

Effective Potentials
Taylor 8.4
Applet: Effective Potentials

Inverse Square Forces:
Kepler's First Law
Applet: Effective Potentials w/ Orbits

Orbits Summary



06 M 5/9

Scattering

07 T 5/10

Eigenstates on a Quantum Ring
Course Notes 14
McIntyre 7.5

08 W 5/11

Probabilities for the Ring from Multiple Representations
Video: Matrix Representations for a Particle on a Ring
Video: Position Representations for a Particle on a Ring
Video: Degeneracy on the Ring
Video: Vector Spaces
Video: Inner Products
Video: Exponential Form of Fourier Series, aka Quantum States on a Ring



09 Th 5/12

Meaning of the Wave Function

10 F 5/13

Time Dependence Review

Time Dependence on a Ring
State on a Ring Geogebra Applet



11 M 5/16

Midterm

12 T 5/17

To prepare for class:
Review Power Series
Power Series Review
Review Power Series
GMM: Power Series

Math Bits:
Series Solutions
Power Series Solutions: Method/Example

13 W 5/18

Power Series Theorems
Power Series Solutions: Theorems

Series Solutions for Legendre Polynomials
McIntyre 7.6.1

Properties of Legendre Polynomials
Wikipedia article on Legendre Polynomials



14 Th 5/19

Math Bits:
Sturm-Liouville Theory
Course Notes 4
GMM: Sturm-Liouville Theory
Video: Introduction to Sturm-Liouville Theory

Math Bits:
Legendre Polynomial Series
GMM: Legendre Polynomial Series

15 F 5/20

Example:
Particle in a 2-D Quantum Box
Simulation: 2-D Rectangular Box
Simulation: 2-D Circular Box

Example:
Quantum Cylinder



16 M 5/23

Math Bits:
PDEs in Physics
GMM: Important PDEs in Physics GMM: Classification of PDEs
Video: Classification of PDEs

Separation of Variables
Rectangular
(Review)

Math Bits:
Separation of Variables in Curvilinear Coordinates
McIntyre 7.4
GMM: Separation of Variables

17 T 5/24

Separating out Center-of-Mass: Quantum
McIntyre 7.1

Schrödinger's Equation:
Spherical Symmetry
Course Notes 10-13
McIntyre 7.2

Rigid Rotor
McIntyre 7.4
McIntyre 7.6
Video: Separation of Variables for the Rigid Rotor
Course Notes 15-17

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

Legendre's Associated Equation
McIntyre 7.6.2

Spherical Harmonics:
Properties
McIntyre 7.6.4

Spherical Harmonics:
Visualization
Video: Description of Spherical Harmonics
McIntyre 7.6.5

Symmetries, Parity, Degeneracy

18 W 5/25

Quantum States of the Rigid Rotor



19 Th 5/26

Orbital Angular Momentum:
Spin 1 revisited
McIntyre 7.3

Commutation Relations

Raising and Lowering Operators
Griffiths 4.3

20 F 5/27

Time Dependence
McIntyre 7.6.3

Math Bits:
Boundary & Initial Conditions
GMM: Boundary & Initial Conditions on PDEs in Physics



21 M 5/30
MEMORIAL DAY
No Class

22 T 5/31

The Radial Equation
McIntyre 8.1-8.4
Krane: Class Notes 3

Asymptotic Behavior

Laguerre Polynomals

Radial Functions

Visualizing Radial Functions
Video: Visualization of Radial Functions

23 W 6/1

Hydrogen Atom Wave Functions
McIntyre 8.5-8.6

Calculations on Hydrogen Atom States



24 Th 6/2

Hydrogen Spectra
McIntyre 8.3

Symmetries, Parity, Degeneracy

Hydrogen Atom Visualization of Probability Densities
Video: Interpreting Hydrogen Atom Plots

Classical Limit

Applications

Vector Spaces
Inner Products
Video: Vector Spaces
Video: Inner Products

25 F 6/3

Review

Midterm Revisit



26 M 6/6 Noon
FINAL EXAM