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===== Summary Learning Goals =====

**Goal 1:**  Predict and contrast the results of Stern Gerlach experiments for classical and quantum particles

**Goal 2:**  Use linear algebra concepts (inner products, change of basis, eigenvectors, etc.) to describe quantum systems

**Goal 3:**  Calculate probabilities, expectations values, and uncertainties for various experiments

**Goal 4:**  Describe the effects of a measurement on the state vector for a quantum system

**Goal 5:**  Make predictions about the time evolution of quantum states and probabilities

**Goal 6:**  Appreciate quantum ''spookiness''(??) (Distinguish purely quantum behavior from classical)

**Goal 7:**  Use spin-1/2 systems as a productive analogy for generic quantum systems and the infinite square well

**Goal 8:**  Use and explain the connections between Dirac, matrix, and wavefunction notations to perform calculations



===== Course Schedule of Topics =====




==== Classical Review: Spin and Magnetic Moment ====

  : **Hour 1: Administrative **

  : **Hour 2: [[..:sporder20:spclangmom |  Classical Angular Momentum ]] **
    * SWBQ: Review Angular Momentum
    * SWBQ: Spinning Top Precession
    * Bicycle wheel precession demo (background for Spin Precession)

  : **Hour 3: [[..:sporder20:spmagmom | Magnetic Moment ]] **
    * Force & Torque on a magnetic moment
    * SWQB Sequence: Spinning Charged Sphere in a Magnetic Field
    * Intro to Stern-Gerlach Experiment

==== Math Bits: Linear Algebra and Complex Numbers ====

  : **Hour 4 [[..:sporder20:spmatrix | Matrix Manipulations and Representing Complex Numbers ]] **

  : **Hour 5 [[..:sporder20:spcomplex | Complex Numbers ]] **

  : **Hour 6 [[..:sporder20:splinear | Linear Transformations ]] **
  
  : **Hour 7 [[..:sporder20:spbraket | Bra Ket and Matrix Elements ]] **
  
  : **Hours 8-9 [[..:sporder20:speigen | Eigenvectors and Eigenvalues]] **
  
  : **Hour 10 [[..:sporder20:spspecialmatrix | Special Matricies ]] **



==== Spin Systems ====
  : **Hour 11: [[..:sporder20:spqmmodel | Building a quantum model: Postulates and Experiment ]] **
    *  WCD: What is a model?
    *  WCD: What is a state?
    *  Introduce the State Postulate
    *  SGA: Probabilities of Stern-Gerlach Measurement Simulation
 

  : **Hour 12: [[..:sporder20:spqmstatevectors | Quantum State Vectors and Probability ]] **
    *  Introduce quantum state vector
    *  Probabilities as norm squares of coefficients
    *  The Probability Postulate
    *  Representing quantum states with arms


  : **Hour 13: [[..:sporder20:spNAME | UNNAMED ]] **
    *  Introduce Spin 1 and General Quantum States


  : **Hour 14: [[..:sporder20:spspinstates | Determining Spins State from Data ]]**
    *  Finding coefficients from SG data, in general
    *  Finding $| \pm\rangle_x$ and $| \pm\rangle_y$ from SG data
    *  Real space vs. Hilbert space and visualizing quantum states with graphs and arms


  : **Hour 15: [[..:sporder20:spvectors | Orthogonal and Normal Vectors ]] **
    *  Finding orthogonal vectors
    *  Normalizing quantum state vectors
 
  : **Hour 16: [[..:sporder20:spbases | Bases ]] **
    *  Using different bases to express quantum states 
    *  $| \pm\rangle_n$ in spherical coordinates

  : **Hour 17: [[..:sporder20:spstates | Determining States from Data ]] **
    *
 SGA: Finding Unknown States




==== Operators ====

  : **Hour 18: [[..:sporder20:spoperators | Collapse & Projection Operators ]] **
    *  Projection Operators
    *  The Projection Postulate


  : **Hour 19 [[..:sporder20:spNAME | UNNAMED ]] **
    *  SGA: [[courses:activities:spact:spspin3| Quantum Interferometer]]


  : **Hour 20: [[..:sporder20:spobservables | Observables]] **
    *  Properties of Hermitian Matrices: Orthogonality, Real Eigenvectors
    *  Spin Eigenvalue Equations
    *  SGA: Matrix Form of Spin Operators


  : **Hour 21: [[..:sporder20:sptotalspin | Total Spin ]] **
    *  Calculating matrix elements of operators
    *  Spin Vector $\vec{S}$
    *  $\hat{S}^2$ operator


  : **Hour 22: [[..:sporder20:speprparadox | (Optional) EPR Paradox ]] **


==== Measurement ====

  : **Hour 23: [[..:sporder20:spstatistics | Statistics ]] **
    *  Average and Standard Deviation
    *  Expectation Value and Uncertainty

  : **Hour 24: [[..:sporder20:spcommutation | Communtation ]] **
    *  Commutation

  : **Hour 25: [[..:sporder20:spuncertainty | Uncertainty Relations ]]**
    *  Uncertainty Relations


==== Time Dependence ====

  : **Hour 26: [[..:sporder20:spschrodinger | Solving Schrodinger ]] **
    *  For Time Independent Hamiltonians

  : **Hour 27: [[..:sporder20:spstationarystates | Stationary States]] **
    *  SGA: Conditions for Time Dependent Probabilities

  : **Hour 28: [[..:sporder20:spprecession | Precession ]] **
    *  Spin Precession

  : **Hour 29: [[..:sporder20:sp | UNNAMED ]] **
    *  Rabi Oscillations


==== Intro to Spatial Potentials ====

  : **Hour 30: [[..:sporder20:spwavefunctions | Classical Probability Density ]] **
    * 
    * 

  : **Hour 31: [[..:sporder20:spwavefunctions | Wavefunction Representation ]] **
    *  Wavefunctions
    *  Translating between Dirac Notation and Wavefunction language

  : **Hour 32: [[..:sporder20:spdiffoperators | Differential Operators & Eigenfunctions ]] **
    *  SGA: Operators and Functions

  : **Hours 33: [[..:sporder20:spisw | Infinite Square Well ]]**
    * Separate Variables
    * Solve Spatial Diff. Eq.
    * Apply Boundary Conditions & Normalization
 
   : **Hour 34: [[..:sporder20:spisweigen | Energy Eigenstates of Infinite Square Well ]]**
    * Interpret Eigenstates
    * Covariation with parameters
    * Visualize with PhET
    
   : **Hour 35: [[..:sporder20:spiswevolution | Time Evolation of Infinite Square Well ]]**
     * Solve Time Dependence
     * Visualize with PhET
     * Review Stationary States
    
   : **Hours 36-37: [[..:sporder20:spiswreps | Representations of ISW ]]**
     * SGA: Representations of ISW Superposition States



==== Review ====

  : **Hour 38: Review **
 

==== Optional Topics ====
//Can be skipped//

    *  Neutrino Oscillation (SGA) //40 min// FIXME
    *  Magnetic Resonance
    *  EPR Paradox
    *  Schrodinger's Cat