Table of Contents
This link will take you to the original version of the Central Forces page.
Unit: Math Bits - Power Series Solutions to ODEs
- Hour 1: Math Bits - Series Solutions
- Summation Notation and Derivatives
- Solving a Differential Equation with Power Series
- Hour 2: Math Bits - Change of Variables
- Changing Independent Variables
- Changing Dependent Variables
- Optional: Solving the Hermite Equation
- Hour 3: Math Bits - Legendre's Equation
- Solving Legendre's Equation
- Introduction to Special Functions
Unit: Classical Central Forces
- Hour 4: Systems of Particles
- Center of Mass
- Kinesthetic Activity: Survivor Outer Space
- Reduced Mass
- Hour 5: Classical Angular Momentum
- Introduction to Angular Momentum
- Small Whiteboard Activity: Air Table
- Hour 6: Kinematics in Polar Coordinates
- 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
- Hours 9-10: Effective Potentials & Orbital Motion
- 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
- Hour 16: Time Dependence on a Ring
- Energy Eigenstates, Superpositions, and Time Dependence
- Mathematica Activity: Visualizing Time Dependence
Unit: Math Bits - Boundary Value Problems
- Hours 17-18: Math Bits - Particle in a 2-D Box
- 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
- Hours 19-20: Math Bits - Legendre Polynomials
- 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
- Hour 23: Spherical Harmonics
- Spherical Harmonics
- Kinesthetic Activity : Visualizing Spherical Harmonics
- Hour 24-25: QM States for Rigid Rotor
- Spherical Harmonic Series
- Mathematica Activity : Plotting Spherical Harmonic Superpositions
- Hour 26: Time Dependence for Rigid Rotor
- This topic needs new activities
- Review of Commutation
- Angular Momentum Operators
- Hour 28: Raising and Lowering Operators
Unit: The Hydrogen Atom
- Hour 29: The Radial Equation
- 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
- Hour 32: The Classical Limit
- This topic needs more content
- Hours 33-34: Applications of Hydrogen Atom States
- Where Is the Electron?
- This topic needs more content
- Hour 35: Review