Paradigms in Physics: Quantum Fundamentals | 2022-NoTerm

Course Name
Paradigms in Physics: Quantum Fundamentals
Course Number
ph425
Year/Term
NoTerm-2022
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 2/7
Welcome to QF!
Magnetic Moment
Stern-Gerlach Experiment: Measuring Electron Spin

Some Stern-Gerlach History

McIntyre 1.1.0

New Row
Day 2 Tu 2/8
Explore the Stern-Gerlach Experiment
Intro to Stern-Gerlach Experiments 1

SPINS Simulation

Statistical Description of Stern-Gerlach Experiments

Quantum State are Vectors
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 2/9 Math Bits
Review: Complex Numbers: Rectangular Form
Complex Numbers GMM 2.1-2.4
Khan Academy: Complex Numbers
HW 1
HW 1 (pdf)
Circle Trig Practice
Circle Trig Practice (pdf)
Complex Number Practice
Complex Number Practice (pdf)
Complex Conjugation
Norm
Algebra with Complex Numbers
Review: Circle Trig

Review Trig Functions

Trig Tour PhET

Complex Numbers: Exponential Form
Complex Numbers GMM 2.5-2.6
Day 4 Th 2/10 Math Bits
Components of Vectors
Describing a Vector with 2 Different Coordinate Systems
Inner Products
Representations for Finding Components
Bra-ket (Dirac) Notation
$|\pm\rangle$ Forms an Orthonormal Basis
Bra-Ket Notation GMM 3.7
Expanding a Complex-Valued Vector in a Basis
Expanding a Complex-valued Vector in a Basis
Abstract Vector Spaces and Inner Products
(Optional, Advanced)
Vector Spaces GMM Chap. 4
Inner Product of a Complex Vector
Day 5 F 2/11
Inner Product of a Complex Vector
HW 2
HW 2 (pdf)
Review the Anatomy of SG Experiments
The Probability Postulate
McIntyre 1.2
Multiple Representations of Quantum States
Day 6 M 2/14
Practice Probability Postulate & Normalization
Determining Spin from Experiments
Spins Reference Sheet
Multiple Representations of Quantum States
Relative & Overall Phase
Day 7 Tu 2/15
Determining Spin from Experiments
Finding Unknown States Leaving the Oven in a Spin-$\frac{1}{2}$ System
Multiple Representations of Quantum States
Day 8 W 2/16 Mathbits
Review: Operations with Matrices
Operations with Matrices GMM 3.1-3.9
HW 3
HW 3 (pdf)
Matrix Practice
Matrix Practice (pdf)
More Operations with Matrices
Transpose GMM 3.4
Hermitian Adjoint GMM 3.5
Linear Transformations
Linear Transformations
Day 9 Th 2/17 MathBits
Diagonalization
Change of Basis GMM 6.6
Day 10 F 2/18 Math Bits
Finding Eigenvectors & Eigenvalues
Finding Eigenvectors and Eigenvalues
Eigenvectors & Eigenvalues GMM 5.1-5.4
HW 4
HW 4 (pdf)
Eigenvectors Practice
Eigenvectors Practice (pdf)
Eigenbases
Eigenbases GMM 5.7
Day 11 M 2/21
Eigenbases
GMM: Eigenbases
Properties of Hermitian Matrices
Hermitian Matrices GMM 6.1-6.4
Day 12 Tu 2/22
Intro to Higher Spin Systems
Projection Operators
Outer Product of a Vector on Itself
McIntyre 2.2-2.4
Changing Bases with a Completeness Relation
Changing Spin Bases with a Completeness Relation
Completeness Relation/
Matrix Decompositions GMM 6.9
Day 13 W 2/23
General Quantum Systems
HW 5
HW 5 (pdf)
The Projection Postulate
Quantum Interferometer
Spin-1 Interferometer
Day 14 Th 2/24
Quantum Interferometer Cont.
Quantum Operators
Constructing the Spin Operators
Finding Matrix Elements
Finding Matrix Elements
Expectation Value & Uncertainty
McIntyre 2.5, 3.1
The Squared Spin Operator
Day 15 F 2/25
Commutation
Finding if $S_{x}, \; S_{y}, \; and \; S_{z}$ Commute
HW 6
HW 6 (pdf)
Day 16 M 2/28
Quantum Expectation Values
Quantum Expectation Values
Quantum Uncertainty
Day 17 Tu 3/1
Solving the Schrodinger Equation & Time Evolution
More Time Evolution
Day 18 W 3/2
Spin Precession in a Uniform Magnetic Field
Time Evolution of a Spin-1/2 System
HW 7
HW 7 (pdf)
Day 19 Th 3/3
Introduction to Wavefunctions
Day 20 F 3/4
HW 8
HW 8 (pdf)
Day 21 M 3/7
The Infinite Square Well
McIntyre 5.3-5.4
Day 22 Tu 3/8
Wavefunctions
Operators & Functions
McIntyre 5.1-5.2
Day 23 W 3/9
Time Evolution of a particle in an Infinite Square Well

QuVis Simulations of the Time Development of Infinite Well Quantum States

Bound States PhET

HW 9
HW 9 (pdf)
Day 24 Th 3/10
Quantum Spookiness
Day 25 F 3/11
Representations of the Infinite Square Well
Representations of the Infinite Square Well
HW 10
HW 10 (pdf)
Final Exam Review Guide
Review
For Fun: Nature Milestones in Spin
3/17 Th noon-2pm
Final Exam
Classical Spin
Force on a Current Loop
Dirac Representations of Operators: The Decomposition Theorem