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

Hour 1: Administrative

Hour 2: Classical Angular Momentum

• SWBQ: Review Angular Momentum
• SWBQ: Spinning Top Precession
• Bicycle wheel precession demo (background for Spin Precession)

Hour 3: Magnetic Moment

• Force & Torque on a magnetic moment
• SWQB Sequence: Spinning Charged Sphere in a Magnetic Field
• Intro to Stern-Gerlach Experiment

Hour 4 Matrix Manipulations and Representing Complex Numbers

Hour 5 Complex Numbers

Hour 6 Linear Transformations

Hour 7 Bra Ket and Matrix Elements

Hours 8-9 Eigenvectors and Eigenvalues

Hour 10 Special Matricies

Hour 11: 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: 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: UNNAMED

• Introduce Spin 1 and General Quantum States

Hour 14: 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: Orthogonal and Normal Vectors

• Finding orthogonal vectors
• Normalizing quantum state vectors

Hour 16: Bases

• Using different bases to express quantum states
• $| \pm\rangle_n$ in spherical coordinates

Hour 17: Determining States from Data

SGA: Finding Unknown States

Hour 18: Collapse & Projection Operators

• Projection Operators
• The Projection Postulate

Hour 19 UNNAMED

• SGA: Quantum Interferometer

Hour 20: Observables

• Properties of Hermitian Matrices: Orthogonality, Real Eigenvectors
• Spin Eigenvalue Equations
• SGA: Matrix Form of Spin Operators

Hour 21: Total Spin

• Calculating matrix elements of operators
• Spin Vector $\vec{S}$
• $\hat{S}^2$ operator

Hour 22: (Optional) EPR Paradox

Hour 23: Statistics

• Average and Standard Deviation
• Expectation Value and Uncertainty

Hour 24: Communtation

• Commutation

Hour 25: Uncertainty Relations

• Uncertainty Relations

Hour 26: Solving Schrodinger

• For Time Independent Hamiltonians

Hour 27: Stationary States

• SGA: Conditions for Time Dependent Probabilities

Hour 28: Precession

• Spin Precession

Hour 29: UNNAMED

• Rabi Oscillations

Hour 30: Classical Probability Density

Hour 31: Wavefunction Representation

• Wavefunctions
• Translating between Dirac Notation and Wavefunction language

Hour 32: Differential Operators & Eigenfunctions

• SGA: Operators and Functions

Hours 33: Infinite Square Well

• Separate Variables
• Solve Spatial Diff. Eq.
• Apply Boundary Conditions & Normalization

Hour 34: Energy Eigenstates of Infinite Square Well

• Interpret Eigenstates
• Covariation with parameters
• Visualize with PhET

Hour 35: Time Evolation of Infinite Square Well

• Solve Time Dependence
• Visualize with PhET
• Review Stationary States

Hours 36-37: Representations of ISW

• SGA: Representations of ISW Superposition States

Hour 38: Review

Can be skipped

• Neutrino Oscillation (SGA) 40 min
• Magnetic Resonance
• EPR Paradox
• Schrodinger's Cat