### 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 Add this activity

• Kepler's Second Law CAM added the next two bullets
• Angular Momentum and Kinetic Energy in Polar Coordinates
• Conic Sections
• Mathematica Activity: Plotting Conic Sections 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

• This topic needs more content
Hour 22: Holiday
• Spherical Harmonics
• Kinesthetic Activity : Visualizing Spherical Harmonics
• Spherical Harmonic Series
• Mathematica Activity : Plotting Spherical Harmonic Superpositions
• 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
• This topic needs more content
• Where Is the Electron?
• This topic needs more content
Hour 35: Review

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