Introduction to Quantum Mechanics:
Mathematics W4392
(Spring 2014)
Tuesday and Thursday 4:10-5:25pm
Mathematics 307
This will be a continuation of the fall course Math
W4391 covering more advanced material.
This course is open to both undergraduate and graduate
students. It can be taken independently and in addition to any
of the Physics department courses on quantum mechanics.
Lecture Notes
Note: The lecture notes for the course have been turned
into a book, available here.
I've removed the old lecture notes and problem sets, since
better versions of this material are incorporated in the book.
A very detailed set of notes for this course is under
development, with the latest version always available here.
During the fall semester the course covered the first 20 chapters
of those notes. Before each class, please try and read the
chapter in the syllabus announced for that class and come prepared
with questions about whatever you don't understand. I hope
to devote much of the time in each class to going over material
students are finding confusing, rather than repeating everything
that is in the notes.
Problem Sets
There will be problem sets due roughly every other week, one
of which will be a take-home midterm exam, and a required final
project.
Syllabus
Tuesday, January 20: Review of fall semester, overview of
topics to be covered.
Thursday, January 21: The harmonic oscillator and the
Heisenberg group (chapter 21).
Tuesday, January 27: University closed due to "blizzard".
Thursday, January 29: Squeezed and coherent states of the
harmonic oscillator (chapter 21).
Tuesday, February 3: The harmonic oscillator and the
metaplectic representation (chapter 22).
Thursday, February 5: The harmonic oscillator and the
metaplectic representation in d dimensions (chapter 23).
Tuesday, February 10: The fermionic oscillator (chapter 24),
Weyl and Clifford algebras (chapter 25).
Thursday, February 12: Clifford algebras and geometry (chapter
26).
Tuesday, February 17: Anticommuting variables and
pseudo-classical mechanics (chapter 27).
Thursday, February 19: Fermionic quantization and spinors
(chapter 28).
Tuesday, February 24: Fermionic quantization and spinors
(chapter 28) and Summary of bosonic/fermionic parallels (chapter
29).
Thursday, February 26: The Dirac operator (chapter 31).
Tuesday, March 3: Lagrangian methods and the path integral (chapter
32).
Thursday, March 5: Infinite-dimensional phase spaces, survey
of field quantization. Multi-particle systems (chapter 34 and 37)
Tuesday, March 10: Non-relativistic quantum fields (chapters
34 and 35)
Thursday, March 12: More on non-relativistic quantum fields
(chapter 35)
Tuesday, March 24: Minkowski space and the Lorentz group
(chapter 38)
Thursday, March 26: Representations of the Lorentz group
(chapter 39)
Tuesday, March 31: The Poincare group its representations
(chapter 40)
Thursday, April 2: The Klein-Gordon equation and scalar
quantum fields (chapter 41)
Tuesday, April 7: More on scalar quantum fields
Thursday, April 9: Quantum fields and symmetries (chapters 36
and 42)
Tuesday, April 14: U(1) gauge symmetry (chapter 43)
Thursday, April 16: Quantization of the electromagnetic field
(chapter 44)
Tuesday, April 21: Spin 1/2 particles (chapter 45)
Thursday, April 23: More on spin 1/2 particles
Tuesday, April 28: Introduction to the Standard Model (chapter
46)
Thursday, April 30: Student talks.
Tuesday, May 5: Student talks.
Thursday, May 7: Student talks.
Previous Courses
Introduction
to Quantum Mechanics, Fall 2012: Math W4391
Introduction
to Quantum Mechanics, Spring 2013: Math W4392