PHYS 684: Quantum Mechanics I

Announcements

Dec. 6, Last lecture. Pick up your homework.
Dec. 20, Final exam, 7:30-10:15pm, in class, close-book.

Time and Location

Monday 7:20-10:00 pm, Aug 30 to Dec 21, Science and Technology I, Rm 310

Office hours

Monday and Friday 2:00-3:00 pm, Science and Technology I, Rm 363B

Grades

Homework (50%) + Midterm (25%) + Final exam (25%)
Homework is due each week before the start of each class. Late homework will not be graded. The solutions will be distributed electronically. Both midterm and final exam will be in-class, closed book. The difficult level of exam problems is comparable to homework.

Course Goal and Prerequisites

This course will cover the fundamentals of quantum mechanics (QM) including its concepts and principles, its mathematical structure and applications. It assumes that you had some previous exposure to quantum mechanics (either in Modern Physics, Phys 308, or undergraduate QM, Phys 502). If QM is completely new to you, you are strongly encouraged to work through Griffith, Introduction to Quantum Mechnics, or its equivalent before coming into the class or in parallel to the lectures.

Topics

  1. The leap from classical to quantum
  2. Linear vector space in Dirac notation
  3. Hilbert space of continuous functions
  4. Postulates of quantum mechanics
  5. Quantum dynamics
  6. QM in one dimension (2 lectures)
  7. Continuous symmetries: translation and rotation
  8. Spectrum of angular momentum
  9. Rotationally invariant potentials
  10. Discrete symmetries
  11. QM of many particles
  12. Density matrix and entanglement [optional]

Textbook

Principles of Quantum Mechanics, by R. Shankar, 2nd Ed., Springer 1994

There are many excellent textbooks to supplement Shankar, e.g.,
Modern quantum mechanics, by J. J. Sakurai, revised Ed., Addison-Wesley, 1994
Quantum mechanics: non-relativistic theory, L. D. Landau and E. M. Lifshitz