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Unit: Math Bits - Power Series Solutions to ODEs

  • Summation Notation and Derivatives
  • Solving a Differential Equation with Power Series
  • Changing Independent Variables
  • Changing Dependent Variables
  • Optional: Solving the Hermite Equation
  • Solving Legendre's Equation
  • Introduction to Special Functions

Unit: Classical Central Forces

  • Center of Mass
    • Kinesthetic Activity: Survivor Outer Space
  • Reduced Mass
  • Introduction to Angular Momentum
    • Small Whiteboard Activity: Air Table
  • Polar Coordinates
  • Vectors
    • Small Group Activity: Velocity and Acceleration in Polar Coordinates FIXME Add this activity

  • Kepler's Second Law FIXME CAM added the next two bullets
  • Angular Momentum and Kinetic Energy in Polar Coordinates
  • Conic Sections
    • Mathematica Activity: Plotting Conic Sections FIXME CAM moved this activity
  • Equations of Motion
  • QUIZ
  • Conservation and Orbital Shape
  • Effective Potentials
    • Kinesthetic Activity: Interpreting Effective Potential Plots
  • Trajectories
Hours 11-12: Scattering
  • What Is Scattering?
  • Cross-section Geometry
  • Differential Cross Sections
    • Small Group Activity: Hard Sphere

Unit: Quantum Central Forces in One Dimension (The Ring Problem)

  • Review of Hamiltonians
  • Separation of Variables
Hours 14-15: QM States on a Ring
  • QUIZ
  • Energy Eigenstates for the Ring
  • Angular Momentum for the Ring
    • Small Group Activity: The Ring
  • Energy Eigenstates, Superpositions, and Time Dependence
    • Mathematica Activity: Visualizing Time Dependence

Unit: Math Bits - Boundary Value Problems

  • PDE Solution with 2 Space and 1 Time Variables
  • Applying Boundary Conditions to PDE Solutions
    • Small Group Activity: Infinite Square Well Squared
  • Degenerate Solutions to PDEs
  • Properties of Legendre Polynomials
    • Mathematica Activity: Legendre Polynomial Expansions
  • Finding Legendre Series Coefficients

Unit: The Quantum Rigid Rotor

  • FIXME This topic needs more content
Hour 22: Holiday
  • Spherical Harmonics
    • Kinesthetic Activity : Visualizing Spherical Harmonics
  • Spherical Harmonic Series
    • Mathematica Activity : Plotting Spherical Harmonic Superpositions
  • FIXME This topic needs new activities
  • Review of Commutation
  • Angular Momentum Operators

Unit: The Hydrogen Atom

  • QUIZ
  • Solving the Radial Wave Function
    • Mathematica Activity: Visualizing Radial Wave Functions
Hours 30-31: The Hydrogen Atom
  • The Full Solution
    • Mathematica Activity: Visualizing Probability Density
  • Quantum Calculations
  • FIXME This topic needs more content
  • Where Is the Electron?
  • FIXME This topic needs more content
Hour 35: Review

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