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

• SWBQ: Review Angular Momentum
• SWBQ: Spinning Top Precession
• Bicycle wheel precession demo (background for Spin Precession)
• Force & Torque on a magnetic moment
• SWQB Sequence: Spinning Charged Sphere in a Magnetic Field
• Intro to Stern-Gerlach Experiment

Spin Systems

• WCD: What is a model?
• WCD: What is a state?
• Introduce the State Postulate
• SGA: Probabilities of Stern-Gerlach Measurement Simulation
• 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
• 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
• Finding orthogonal vectors
• Normalizing quantum state vectors
Hour 16: Bases
• Using different bases to express quantum states
• $| \pm\rangle_n$ in spherical coordinates

SGA: Finding Unknown States

Operators

• Projection Operators
• The Projection Postulate
Hour 19 UNNAMED
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

Measurement

Hour 23: Statistics
• Average and Standard Deviation
• Expectation Value and Uncertainty
• Commutation
• Uncertainty Relations

Time Dependence

• For Time Independent Hamiltonians
• SGA: Conditions for Time Dependent Probabilities
Hour 28: Precession
• Spin Precession
Hour 29: UNNAMED
• Rabi Oscillations

Intro to Spatial Potentials

• Wavefunctions
• Translating between Dirac Notation and Wavefunction language
• SGA: Operators and Functions
• Separate Variables
• Solve Spatial Diff. Eq.
• Apply Boundary Conditions & Normalization
• Interpret Eigenstates
• Covariation with parameters
• Visualize with PhET
• Solve Time Dependence
• Visualize with PhET
• Review Stationary States
• SGA: Representations of ISW Superposition States

Hour 38: Review

Optional Topics

Can be skipped

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

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