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

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.

Problem Set 9 (due Thursday, February 5).
Problem Set 10 (due Tuesday, February 17).
Problem Set 11 (due Tuesday, March 3).
Problem Set 12 (due Tuesday, March 24).
Problem Set 13 (due Tuesday, April 7).
Problem Set 14 (due Tuesday, April 21).

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