8.321 | Fall 2017 | Graduate
Quantum Theory I


Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session


8.05 Quantum Physics II


This is the first semester of a two-semester graduate-level subject on quantum theory.

Topics Covered

  1. Fundamental concepts
    1. Kets, bras, and operators
    2. Measurements, observables, and uncertainty relations
    3. Change of basis
    4. Position, momentum
  2. Quantum dynamics
    1. Schrödinger and Heisenberg pictures
    2. Schrödinger equation and elementary solutions
    3. Path integral formulation
    4. Coupling to electromagnetic fields, Aharanov-Bohm effect
  3. Composite systems
    1. Tensor product states; quantum entanglement
    2. Density matrices
    3. Quantum information
  4. Symmetries in quantum mechanics
    1. Continuous symmetries and conservation laws
    2. Angular momentum
      1. Angular momentum algebra, SO(3) vs SU(2)
      2. Irreducible representations of SU(2) and SO(3)
      3. Addition of angular momentum
    3. Discrete symmetries: Parity and time reversal
  5. Approximation methods
    1. Perturbation theory
    2. Adiabatic approximation, Berry phase
    3. Semiclassical approximation
    4. Variational methods


Sakurai, Jun John, and Jim Napolitano. Modern Quantum Mechanics. Cambridge University Press, 2017. ISBN: 9781108422413. [Preview with Google Books]

The Solvay Meetings and the Development of Quantum Mechanics. Niels Bohr at the occasion of the 12th Solvay Conference in Physics, 9–14. October 1961. “Quantum Theory of Fields (PDF).”

Kleppner, Daniel, and Roman Jackiw. “One Hundred Years of Quantum Physics.” Science 289, no. 5481 (2000): 893–8.


The course grade is based entirely on the homework assignments.

Course Info
As Taught In
Fall 2017
Learning Resource Types
assignment Problem Sets
notes Lecture Notes
grading Exams