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).

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
Tuesday, March 10:  Non-relativistic quantum fields: field quantization and dynamics.
Thursday, March 12:  Symmetries and non-relativistic quantum fields

Previous Courses

Introduction to Quantum Mechanics, Fall 2012: Math W4391
Introduction to Quantum Mechanics, Spring 2013: Math W4392