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[[cforder20premike|This link will take you to the original version of the Central Forces page.]]

==== Unit:  Math Bits - Power Series Solutions to ODEs ====

  : **Hour 1: [[..:order20:cforder20:cfmbseries|Math Bits - Series Solutions]] **
    * Summation Notation and Derivatives
    * Solving a Differential Equation with Power Series
  : **Hour 2: [[..:order20:cforder20:cfmbcov|Math Bits - Change of Variables]] **
    * Changing Independent Variables
    * Changing Dependent Variables
    * Optional: Solving the Hermite Equation
  : **Hour 3: [[..:order20:cforder20:cfmblegeq|Math Bits - Legendre's Equation]] **
    * Solving Legendre's Equation
    * Introduction to Special Functions

==== Unit:  Classical Central Forces ====




  : **Hour 4: [[..:order20:cforder20:cfsystems|Systems of Particles]]**
    * Center of Mass
      * //Kinesthetic Activity: Survivor Outer Space//
    * Reduced Mass

  : **Hour 5: [[..:order20:cforder20:cfclassical|Classical Angular Momentum]]**
    * Introduction to Angular Momentum
      * //Small Whiteboard Activity: Air Table//

  : **Hour 6: [[..:order20:cforder20:cfkinematics|Kinematics in Polar Coordinates]]**
    * 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

  : **Hour 7: [[..:order20:cforder20:cfconic|Conic Sections and Kepler's First Law]]**
    * Conic Sections
      * //Mathematica Activity: Plotting Conic Sections//  FIXME  CAM moved this activity
    * Equations of Motion

  : **Hour 8: [[..:order20:cforder20:cfenergy|Energy and Angular Momentum Conservation]]** 
    * QUIZ
    * Conservation and Orbital Shape


  : **Hours 9-10: [[..:order20:cforder20:cfeffpot|Effective Potentials & Orbital Motion]]**
    * Effective Potentials
      * //Kinesthetic Activity: Interpreting Effective Potential Plots//
    * Trajectories

  : **Hours 11-12: [[..:order20:cforder20:cfscattering|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) ====


  : **Hour 13: [[..:order20:cforder20:cfseparation|Separation of Variables in Spherical Coordinates]]**
    * Review of Hamiltonians
    * Separation of Variables


  : **Hours 14-15: [[..:order20:cforder20:cfqmring|QM States on a Ring]]**
    * QUIZ
    * Energy Eigenstates for the Ring
    * Angular Momentum for the Ring
      * //Small Group Activity: The Ring//


  : **Hour 16: [[..:order20:cforder20:cftimedepring|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: [[..:order20:cforder20:cfmb2d|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: [[..:order20:cforder20:cfmblps|Math Bits - Legendre Polynomials]] **
    * Properties of Legendre Polynomials
      * //Mathematica Activity: Legendre Polynomial Expansions //
    * Finding Legendre Series Coefficients



==== Unit: The Quantum Rigid Rotor ====


  : **Hour 21: [[..:order20:cforder20:cfqmrigid|QM Rigid Rotor Intro, Associated Legendre Polynomials]]**
    * FIXME This topic needs more content

  : **Hour 22: Holiday **

  : **Hour 23: [[..:order20:cforder20:cfsphereharm|Spherical Harmonics]]**
    * Spherical Harmonics
      * //Kinesthetic Activity : Visualizing Spherical Harmonics//

  : **Hour 24-25: [[..:order20:cforder20:cfqmrotor|QM States for Rigid Rotor]]**
    * Spherical Harmonic Series
      * //Mathematica Activity : Plotting Spherical Harmonic Superpositions//



  : **Hour 26: [[..:order20:cforder20:cftimedeprotor|Time Dependence for Rigid Rotor]]**
    * FIXME This topic needs new activities


  : **Hour 27: [[..:order20:cforder20:cfangular|Angular Momentum Commutation Relations]]**
    * Review of Commutation
    * Angular Momentum Operators

 
  : **Hour 28: [[..:order20:cforder20:cfraiselower|Raising and Lowering Operators]]**




==== Unit:  The Hydrogen Atom ====



  : **Hour 29: [[..:order20:cforder20:cfradialeq|The Radial Equation]]**
    * QUIZ
    * Solving the Radial Wave Function
      * //Mathematica Activity: Visualizing Radial Wave Functions//



  : **Hours 30-31: [[..:order20:cforder20:cfhydrogen|The Hydrogen Atom]]**
    * **The Full Solution**
      * //Mathematica Activity: Visualizing Probability Density//
    * Quantum Calculations




  : **Hour 32: [[..:order20:cforder20:cfclassicallimit|The Classical Limit]]**
    * FIXME This topic needs more content


  : **Hours 33-34: [[..:order20:cforder20:cfhydrogenapps|Applications of Hydrogen Atom States]]**
    * Where Is the Electron?
    * FIXME This topic needs more content

  : **Hour 35: Review **