Introduction to Quantum Mechanics:
Tuesday and Thursday 4:10-5:25pm
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.
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.
There will be problem sets due roughly every other week, one
of which will be a take-home midterm exam, and a required final
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
Tuesday, February 17: Anticommuting variables and
pseudo-classical mechanics (chapter 27).
Thursday, February 19: Fermionic quantization and spinors
Tuesday, February 24: Fermionic quantization and spinors
(chapter 28) and Summary of bosonic/fermionic parallels (chapter
Thursday, February 26: The Dirac operator (chapter 31).
Tuesday, March 3: Lagrangian methods and the path integral (chapter
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
Tuesday, March 24: Minkowski space and the Lorentz group
Thursday, March 26: Representations of the Lorentz group
Tuesday, March 31: The Poincare group its representations
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
Tuesday, April 14: U(1) gauge symmetry (chapter 43)
Thursday, April 16: Quantization of the electromagnetic field
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
Thursday, April 30: Student talks.
Tuesday, May 5: Student talks.
Thursday, May 7: Student talks.
to Quantum Mechanics, Fall 2012: Math W4391
to Quantum Mechanics, Spring 2013: Math W4392