Day
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
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Central Force Definition
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Central Force with no External Forces
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Conservative Forces
Reduced Mass
-
face Reduced Mass Lecture Notes
Taylor 8.2
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Center of Mass for Two Uncoupled Particles
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Reduced Mass
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Sun vs. Jupiter
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Undo Formulas for Reduced Mass (Algebra)
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Undo Formulas for Reduced Mass (Geometry)
Spherical/Polar Coordinates
(Review)
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Angular Momentum and Kinetic Energy in the Center of Mass
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Polar Basis Vectors
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Polar vs. Spherical Coordinates
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Positions and Velocities in Curvilinear Coordinates
Velocity and Acceleration
(Review)
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group Velocity and Acceleration in Polar Coordinates
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face Acceleration in Polar Coordinates
03 W 5/4
Polar Graphs
Circles, Ellipses, Hyperbolas
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Eccentricity
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Lines in Polar Coordinates
04 Th 5/5
Conservation of
Classical Angular Momentum
-
face Conservation of Angular Momentum
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Central Forces are Conservative
Equations of Motion: F=ma
-
face Equations of Motion Lecture Notes
Taylor 8.3, second part
-
Newtonian Mechanics: Central Force
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WQ-Lagrangian Mechanics for a Central Force
Change of Variables
Orbit Shape
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Find Force Law: Logarithmic Spiral Orbit
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Find Force Law: Spiral Orbit
Orbits for Inverse Square Forces
Taylor 8.6-8.7
05 F 5/6
Potentials
Equations of Motion: E=T+U
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face Equations of Motion from Energy Conservation
Effective Potentials
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Hockey
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NASA
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NASA 2
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Scattering
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WQ-Effective Potentials
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Yukawa
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Yukawa 2
Inverse Square Forces:
Kepler's First Law
Orbits Summary
-
face Classical Orbits Summary
06 M 5/9
Scattering
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Hard Cone Scattering
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Solid Angle
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
-
Activity: Representations of Probabilities on the Ring
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Activity: Working with Representations on the Ring
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Energy and Angular Momentum for a Quantum Particle on a Ring Handout
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Normalization of Quantum States
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QM Ring Compare
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QM Ring Function
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QMRingCompareSeparated
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Representations of Probabilities on the Ring
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Ring Function
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Ring Ket Book
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Ring Table
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Working with Representations on the Ring
09 Th 5/12
Meaning of the Wave Function
10 F 5/13
Time Dependence Review
Time Dependence on a Ring
-
Expectation Values for a Particle on a Ring Handout
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Particle on a Ring Time Dependence: Mathematica Notebook
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QM Ring Function with Time Dependence
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QM Ring Time
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QM Ring with Time Dependence
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QMRing_TimeDep_Intro
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Ring Ket
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Superposition States for a Particle on a Ring
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Time Dependence for a Quantum Particle on a Ring
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Visualization of Wave Functions on a Ring
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WQ_Particle_On_The_Ring_I
11 M 5/16
Midterm
-
face Classical Orbits Equation Sheet
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face Quantum Ring Equation Sheet
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face Classical Orbits Summary
12 T 5/17
To prepare for class:
Review Power Series
Power Series Review
Math Bits:
Series Solutions
-
group Power Series Solution of ODEs: Math Example
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Hermite Polynomials
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Laguerre
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Laguerre Polynomials
-
Laguerre Polynomials
-
Legendre
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ODE Power Series Solutions One
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ODE Power Series Solutions Two
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Power Series Solution for Laguerre Polynomials
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Recurrence Math
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Recurrence Relations
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Sum Shift
13 W 5/18
Power Series Theorems
Series Solutions for Legendre Polynomials
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face Series Solutions of Legendre's Equation
McIntyre 7.6.1
Properties of Legendre Polynomials
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face Legendre Polynomials Lecture
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Legendre Polynomial Look Up
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Properties of Legendre Polynomials
14 Th 5/19
Math Bits:
Sturm-Liouville Theory
-
face Sturm-Liouville Theorems
Math Bits:
Legendre Polynomial Series
-
computer Guessing Legendre Coefficients
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face Legendre Polynomial Series Lecture
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computer Expanding a Function in Legendre Polynomials.
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Legendre Polynomial Series for the Sine Function
15 F 5/20
Example:
Particle in a 2-D Quantum Box
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Laplace
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Laplace Practice
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Quantum Particle in a 2-D Box
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Quantum Particle in a 2D Box with Time Dependence
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Quantum Particle in a 2D Box: Complete
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Square 2D
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Square 2D Fourier
Example:
Quantum Cylinder
16 M 5/23
Math Bits:
PDEs in Physics
Separation of Variables
Rectangular
(Review)
Math Bits:
Separation of Variables
in Curvilinear Coordinates
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Laplace's Equation in Polar Coordinates
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Separation of Variables on the Sphere
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
Review:
Change of Variables
-
ODE Change of Independent Variable
Legendre's Associated Equation
McIntyre 7.6.2
Spherical Harmonics:
Properties
McIntyre 7.6.4
-
First Nine Terms
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Harmonics Verify P
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Spherical Harmonics Lookup
Spherical Harmonics:
Visualization
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Quantum State Visualization
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Visualization of a Particle on a Sphere Superpositions
Symmetries, Parity, Degeneracy
18 W 5/25
Quantum States of the Rigid Rotor
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face Quantum Reference Sheet
-
group Probabilities for a Quantum Particle on a Unit Sphere in Spherical Harmonic Functions
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group Finding Coefficients of a Spherical Harmonics Series
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Angular Momentum Probability
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Quantum Numbers on the Sphere
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Rigid Rotor Probabililties Practice
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Sphere
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Sphere Questions
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Sphere Questions: Matrix Notation
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Sphere Table
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Spherical Harmonics Expansion
19 Th 5/26
Orbital Angular Momentum:
Spin 1 revisited
McIntyre 7.3
Commutation Relations
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Angular Momentum Commutation Relations
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WQ_Angular_Momentum_Algebra_I
Raising and Lowering Operators
Griffiths 4.3
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Raising and Lowering Operators for Spin
20 F 5/27
Time Dependence
-
group Quantum Particle on a Unit Sphere in Dirac Notation
McIntyre 7.6.3
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QM Sphere with Time Dependence
Math Bits:
Boundary & Initial Conditions
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
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computer Visualizing Radial Wave Functions
23 W 6/1
Hydrogen Atom Wave Functions
McIntyre 8.5-8.6
Calculations on Hydrogen Atom States
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Bohr Radius
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Eigenvalues for Different Systems
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Hydrogen Atom Representation Matching
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Hydrogen Atom Table
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Hydrogen, Version 1
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Hydrogen, Version 2
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Probability Density from the Density Operator
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SP Hybrid
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SP not Hybrid
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SPHybrid2
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Verify Eigenvalues for a Hydrogen Atom State
24 Th 6/2
Hydrogen Spectra
McIntyre 8.3
Symmetries, Parity, Degeneracy
Hydrogen Atom Visualization of Probability Densities
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Interpreting Hydrogen Atom Plots
Classical Limit
Applications
-
group Probability of Finding an Electron Inside the Bohr Radius
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Dipole Moment
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Forbidden Region
Vector Spaces
Inner Products
25 F 6/3
Review
Midterm Revisit
-
Air Table
-
Effective Potentials: Graphical Version
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Probability Density
26 M 6/6 Noon
FINAL EXAM