Paradigms in Physics: Quantum Fundamentals | 2026-Winter

Course Name
Paradigms in Physics: Quantum Fundamentals
Course Number
ph425
Year/Term
Winter-2026
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
W1 D1 MathBits
Welcome to QF!
The Schrodinger Equation
Imaginary Numbers & The Complex Plane
GMM: The Complex Plane
Complex Numbers: Rectangular Form
Complex Number Arithmetic Practice Rectangular Form
GMM: Algebra with Complex Numbers - Rectangular Form
GMM: Complex Conjugate and Norm
GMM: Division - Rectangular Form
Khan Academy: Complex Numbers
W1 D2 MathBits
Circle Trigonometry (Review)
Clock Trigonometry
GMM: Circle Trigonometry
Review Trig Functions
Trig Tour PhET
Complex Numbers: Polar Form
Complex Numbers: Exponential Form
Using Arms to Visualize Complex Numbers (MathBits)
GMM: Euler's Formula
GMM: Exponential Form
GMM: Algebra with Complex Numbers: Exponential Form
GMM: Visualizing the Exponential Function
GMM: Functions of a Complex Variable
Quantum States as Vectors
Vector Review
Introduction to Bra-ket Notation
GMM: Inner Products for Complex Vectors
McIntyre 1.2
Complex-Valued Vectors
Bra Ket Practice Expanding a Complex-valued Vector in a Basis
Hermitian Adjoints
GMM: Transpose
GMM: Hermitian Adjoint
W1 D3 MathBits
Linear Transformations
Linear Transformations
Interactive visualization of linear transformation
HW 1 (w/ Solution)
HW 1 (pdf)
W1 D4 MathBits
Finding Eigenvectors & Eigenvalues
Finding Eigenvectors and Eigenvalues
GMM: Eigenvectors & Eigenvalues
Eigenvectors Practice (w/ Solution)
Eigenvectors Practice (pdf)
W1 D5 MathBits
Abstract Vector Spaces and Inner Products
GMM: Vector Spaces
HW 2 (w/ Solution)
HW 2 (pdf)
W2 D1
Magnetic Moment
Intro to Magnetic Moment
Force on a Current Loop
Force on a Magnetic Moment Due to an External Magnetic Field
Classical Spin
Review Angular Momentum
Classical Angular Momentum SWBQs
Stern-Gerlach Experiment: Measuring Electron Spin
Magnetic Moment \& Stern-Gerlach Experiments

Some Stern-Gerlach History

McIntyre 1.1.0

W2 D2
Explore the Stern-Gerlach Experiment
Intro to Stern-Gerlach Experiments 1

SPINS Simulation

Statistical Description of Stern-Gerlach Experiments

Two Sequential SG Experiments
Sequential Stern-Gerlach Experiments
McIntyre 1.2
Three Sequential SG Experiments
Stern-Gerlach \& Quantum Eraser
McIntyre 1.2.3
Quantum State are Vectors
The Quantum State Postulate
McIntyre 1.1-1.2
W2 D3
The Probability Postulate
Probability Postulate
McIntyre 1.2
Practice Probability Postulate & Normalization
McIntyre 1.2
Practice Probability Postulate
Probabilities of $S_z$ Measurements for Spin-1/2 in Bra-Ket Notation
Multiple Representations of Quantum States
Multiple Representations of a Quantum State
Multiple Representations of Quantum States
Matrix Notation for Spin States
McIntyre 1.3
W2 D4
Multiple Representations of Quantum States
Relative & Overall Phase
Using Arms to Represent Overall and Relative Phase in Spin 1/2 Systems
Determining Spin from Experiments
Determining $|\pm_x\rangle$ and $|\pm_y\rangle$ in the $S_z$ basis
Spins Reference Sheet
W2 D5
Determining Spin from Experiments
Finding Unknown States Leaving the Oven in a Spin-$\frac{1}{2}$ System
New Row
W3 D1 MLK - No Class
New Row
W3 D2
Projection Operators/Completeness Relations
Outer Product of a Vector on Itself
GMM: Projection Operators
McIntyre 2.2-2.4
New Row
W3 D3
The Projection Postulate
Changing Bases with a Completeness Relation
Changing Spin Bases with a Completeness Relation
GMM: Change of Basis (Bra-Ket Notation)
W3 D4
Quantum Interferometer
Spin-1 Interferometer
McIntyre 1.1.4, 2.2.4
Intro to Higher Spin Systems
Spin-1
McIntyre 2.7
General Quantum Systems
McIntyre 1.4
McIntyre 2.2.1-2 McIntyre 2.8
W3 D5
Dirac Representations of Operators: The Decomposition Theorem
Verify the Form of the Spin Operators
The Squared Spin Operator
McIntyre 2.6
Quantum Operators
Constructing the Spin Operators
McIntyre 2.1
Expectation Value & Uncertainty
McIntyre 2.3, 2.5, 3.1
Properties of Hermitian Matrices
W4 D1
Commutation
Finding if $S_{x}, \; S_{y}, \; and \; S_{z}$ Commute
GMM: Commuting Matrices
W4 D2
Quantum Expectation Values
Quantum Expectation Values
McIntyre 2.3
W4 D3
Quantum Uncertainty
Quantum Uncertainty Lecture
Spin 1/2 Uncertainty Brief
McIntyre 2.3, 2.5
W4 D4
Quantum Uncertainty
Spin Uncertainty Relations
Solving the Schrodinger Equation & Time Evolution
Solving the Schrodinger Equation
McIntyre 3.1
More Time Evolution
QM Time Evolution
Using Arms to Represent Time Dependence in Spin 1/2 Systems
Spin Precession in a Uniform Magnetic Field
Time Evolution of a Spin-1/2 System
McIntyre 3.2
Introduction to Wavefunctions
McIntyre 5.3
W4 D5
Going from Spin to Wavefunction (Modified)
W5 D1
The Infinite Square Well
McIntyre 5.3-5.4
W5 D2
Wavefunctions
Operators & Functions
McIntyre 5.1-5.2
W5 D3
Time Evolution of a particle in an Infinite Square Well
Time Evolution of the ISW

McIntyre 5.5.6, 5.6.6, 5.7

QuVis Simulations of the Time Development of Infinite Well Quantum States

Bound States PhET

W5 D4
Representations of the Infinite Square Well
Representations of the Infinite Square Well
McIntyre 5.4, 5.5.6, 5.6.6, 5.7
W5 D5
Final Exam Review Guide
Review
For Fun: Nature Milestones in Spin
2/9 Monday 7pm-9pm
Final Exam