Paradigms in Physics: Quantum Fundamentals | 2024-Winter

Course Name
Paradigms in Physics: Quantum Fundamentals
Course Number
ph425
Year/Term
Winter-2024
Course Credits
4
Class meeting times
9 hours of lecture/discussion per week for five weeks.
Prerequisites
PH 315 and MTH 264
Course description
Introduction to quantum mechanics through Stern-Gerlach spin measurements. Probability, eigenvalues, operators, measurement, state reduction, Dirac notation, matrix mechanics, time evolution. Quantum behavior of a one-dimensional well.
Topic/Day
Activities
Resources
Homework Due
Day 1 M 2/12
Welcome to QF!
Classical Spin
Review Angular Momentum
Magnetic Moment
Intro to Magnetic Moment
Stern-Gerlach Experiment: Measuring Electron Spin
Magnetic Moment \& Stern-Gerlach Experiments

Some Stern-Gerlach History

McIntyre 1.1.0

Force on a Current Loop
Force on a Magnetic Moment Due to an External Magnetic Field
Day 2 Tu 2/13
Explore the Stern-Gerlach Experiment
Intro to Stern-Gerlach Experiments 1

SPINS Simulation

Statistical Description of Stern-Gerlach Experiments

Quantum State are Vectors
McIntyre 1.1-1.2
Two Sequential SG Experiments
Sequential Stern-Gerlach Experiments
McIntyre 1.2
Three Sequential SG Experiments
Stern-Gerlach \& Quantum Eraser
McIntyre 1.2.3
Day 3 W 2/14 Math Bits
Components of Vectors
Describing a Vector with 2 Different Coordinate Systems
Review: Operations with Matrices
GMM: Operations with Matrices
Day 4 Th 2/15 Math Bits
Review: Complex Numbers: Rectangular Form
Complex Conjugate, Norm
Algebra with Complex Numbers
Complex Number Arithmetic
GMM: The Complex Plane
GMM: Complex Conjugate and Norm
GMM: Algebra with Complex Numbers: Rectangular Form
GMM: Division: Rectangular Form
Khan Academy: Complex Numbers
Complex Number Practice
Complex Number Practice (pdf)
Circle Trigonometry Practice
Circle Trigonometry Practice (pdf)
Components of Vectors Practice
Components of Vectors Practice (pdf)
Review: Circle Trig
Clocks

Review Trig Functions

Trig Tour PhET

Complex Numbers: Exponential Form
Using Arms to Visualize Complex Numbers (MathBits)
GMM: Euler's Formula
GMM: Exponential Form
Components of Vectors
Representations for Finding Components
Day 5 F 2/16
Components of a Complex-valued Vector
Bra-ket (Dirac) Notation
Introduction to Bra-ket Notation
GMM: Inner Products for Complex Vectors
McIntyre 1.2
Hermitian Adjoints
GMM: Transpose
GMM: Hermitian Adjoint
Review the Anatomy of SG Experiments
The Probability Postulate
Probability Postulate
McIntyre 1.2
Multiple Representations of Quantum States
Matrix Notation for Spin States
McIntyre 1.3
Day 6 M 2/19
In-Class Quiz on Matrix Multiplication and Determinants
Multiple Representations of Quantum States
Spin 1/2 with Arms
Day 7 Tu 2/20
Multiple Representations of Quantum States
Practice Probability Postulate & Normalization
McIntyre 1.2
Relative & Overall Phase
Using Arms to Represent Overall and Relative Phase in Spin 1/2 Systems
Day 8 W 2/21
Determining Spin from Experiments
Determining $|\pm_x\rangle$ and $|\pm_y\rangle$ in the $S_z$ basis
Spins Reference Sheet
Day 9 Th 2/22
Determining Spin from Experiments
Finding Unknown States Leaving the Oven in a Spin-$\frac{1}{2}$ System
Day 10 F 2/23 Math Bits
Linear Transformations
Matrix Practice
Matrix Practice (pdf)
Day 11 M 2/26 Math Bits
Projection Operators/Completeness Relations
McIntyre 2.2-2.4
Day 12 Tu 2/27 Math Bits
Finding Eigenvectors & Eigenvalues
GMM: Eigenvectors & Eigenvalues
Properties of Hermitian Matrices
GMM: Hermitian Matrices
GMM: Properties of Hermitian Matrices
Day 13 W 2/28
The Projection Postulate
Quantum Measurement Play
Changing Bases with a Completeness Relation
GMM: Matrix Decompositions
Day 14 Th 2/29
Quantum Interferometer
McIntyre 1.1.4, 2.2.4
Intro to Higher Spin Systems
McIntyre 2.7
General Quantum Systems
McIntyre 1.4
McIntyre 2.2.1-2 McIntyre 2.8
Day 15 F 3/1
In-Class Quiz on Eigenvalues and Eigenvectors
Dirac Representations of Operators: The Decomposition Theorem
Verify the Form of the Spin Operators
The Squared Spin Operator
McIntyre 2.6
Expectation Value & Uncertainty
McIntyre 2.3, 2.5, 3.1
Day 16 M 3/4
Commutation
GMM: Commuting Matrices
Day 17 Tu 3/5
Quantum Expectation Values
McIntyre 2.3
Day 18 W 3/6
Quantum Uncertainty
McIntyre 2.3, 2.5
Day 19 Th 3/7
Quantum Uncertainty
Solving the Schrodinger Equation & Time Evolution
McIntyre 3.1
More Time Evolution
Spin Precession in a Uniform Magnetic Field
McIntyre 3.2
Introduction to Wavefunctions
McIntyre 5.3
Day 20 F 3/8
Day 21 M 3/11
The Infinite Square Well
McIntyre 5.3-5.4
Day 22 Tu 3/12
Wavefunctions
McIntyre 5.1-5.2
Day 23 W 3/13
Time Evolution of a particle in an Infinite Square Well

McIntyre 5.5.6, 5.6.6, 5.7

QuVis Simulations of the Time Development of Infinite Well Quantum States

Bound States PhET

Day 24 Th 3/14
Quantum Spookiness
McIntyre Ch 4.
Representations of the Infinite Square Well
McIntyre 5.4, 5.5.6, 5.6.6, 5.7
Day 25 F 3/15
Final Exam Review Guide
Review
For Fun: Nature Milestones in Spin
3/18 M noon-2pm
Final Exam