• Prerequisite Ideas

• Survivor Outer Space: A kinesthetic approach to introducing Center of Mass (Optional Kinesthetic Activity, 20 minutes)
• Derivation and Explanation of Center of Mass (Lecture, 15 minutes)
• Homework

• Prerequisite Ideas
• Assumptions about Central Force Motion (Lecture, 10 minutes)
• Derivation of Reduced Mass (Lecture, 20 minutes)
• Introduction of Angular Momentum (Lecture, 25 minutes)
• Definition of a Central Force (Lecture, 10 minutes)
• Central Forces on an Air Table (Small Whiteboard Activity, 15 minutes)
• Homework

• Prerequisite Ideas
• Position Vectors in Polar Coordinates (Lecture/Discussion, 15 minutes)
• Plotting Conic Sections (Maple Activity, 25 minutes)

• Velocity and Acceleration in Polar Coordinates (Small Group Activity, 20 minutes)
• Kepler's 2nd Law in Polar Coordinates (Lecture, 5 minutes)
• Homework

• Prerequisite Ideas
• Solution to the Central Force Equation of Motion (Lecture, 30 minutes)
• Finding the Shape of the Orbit (Lecture, 25 minutes)
• Finding the Radial Equation from Conservation of Energy (Lecture, 15 minutes)
• Homework

• Prerequisite Ideas
• Energy and Effective Potential (Lecture, 25 minutes)
• Exploring the Effective Potential (Maple Activity, 45 minutes)
• Interpreting Effective Potential Plots (Kinesthetic Activity, 15 minutes)
• Trajectories in an Attractive Central Potential (Maple/Java Activity, 30 minutes)
• Homework

• Prerequisite Ideas
• Review of Hamiltonians (Optional Lecture, 20 minutes)
• Derivation of the Hamiltonian in terms of the Reduced Mass (Optional Lecture, 20 minutes)
• Separation of Variables (Lecture, 30 minutes)
• Homework

• Prerequisite Ideas
• Finding the Eigenstates of Energy for the Ring (Lecture, 30 minutes)
• Angular Momentum for the Ring (Lecture, 20 minutes)
• Energy and Angular Momentum for a Particle Confined to a Ring (Small Group Activity, 30-90 minutes)
• Time Dependence for a Particle Confined to a Ring (Small Group Activity, 30 minutes)
• Visualizing the Probability Density for a Particle Confined to a Ring(Maple Activity, 30 minutes)
• Superposition States for a Particle Confined to a Ring (Optional Small Group Activity, 20 minutes)
• Expectation Values for a Particle Confined to a Ring (Optional Small Group Activity, 20 minutes)
• Homework

This section may also be found in Math Bits.

• Prerequisite Ideas
• Associated Legendre Polynomials (Lecture, 20 minutes)
• Spherical Harmonics, the Solutions to the Rigid Rotor Problem (Lecture, 20 minutes)
• Visualizing Spherical Harmonics Using a Balloon (Kinesthetic, 30 minutes)
• Plotting the Spherical Harmonics (Maple Activity, 15 minutes)
• Combinations of $Y_{l,m}(\theta,\phi)$ and the Spherical Harmonic Series (Lecture, 25 minutes)
• Finding the Coefficients of a Spherical Harmonic Series (Small Group Activity, 25 minutes)
• Plotting Linear Combinations of Spherical Harmonics (Maple Activity, 15 minutes)
• Spherical Harmonics and the $H$, $L^2$, and $L_z$ Operators (Lecture, 60 minutes)
• Homework

• Prerequisite Ideas
• Solving the Radial Equation (Lecture, 40 minutes)
• Visualizing Radial Wavefunctions (Maple Activity, 20 minutes)
• Homework

• Prerequisite Ideas
• Full Solutions to the Hydrogen Atom (Lecture, 45 minutes)
• Visualizing Hydrogen Probability Densities (Maple Activity, 20 minutes)
• Quantum Calculations on the Hydrogen Atom (Small Group Activity, 30 minutes)
• Probability of Finding an Electron Inside the Bohr Radius (Small Group Activity, 45 minutes)
• The Classical Limit (Lecture, 30 minutes)
• Homework