Physics 215B/C (Winter/Spring 2019)

Physics 215B/C, Graduate Quantum Mechanics, Winter/Spring 2019

Prof. Matthew Fisher 

email: ;
Office: 2305 Kohn Hall
Lectures: Monday, Wednesday 11:00-12:15 pm, Phelps 3505
Office Hours: Wednesday, 2-3pm

Find the course web site thru my personal web site:

Grader/TA: Yaodong Li

Office: 6124 Broida Hall
Office Hours: Tuesday 2-3pm 

Textbooks: The "official" textbook for 215B/C is Sakurai/Napolitano (2nd edition).  There are many good QM books - including Shankar, Gottfried/Yan, Landau-Lifshitz, among others.  However, I am hoping to include some more modern topics (e.g. Quantum Ising model and Majorana Fermions) which are not in these books.  I will try to suggest other reading/books when relevant.

Homework:  Roughly 6-7 homeworks throughout each quarter, available on the course web site.  Homework solutions also posted online.  You are encouraged to work together on the homeworks.

Exams:  None.  Unless requested!

Help/feedback:  In addition to my office hours and Yaodong's office hours, I would be happy to schedule a mutually convenient time to chat about homework or other topics (best arranged by e-mail).  I would greatly appreciate feedback on any aspect of the course, anytime throughout the quarter.  


215B Problem Sets



215B Problem Solutions



215C Problem Sets


215C Problem Solutions



SYLLABUS for 215B 

2-State Quantum System (brief review):

  • Measurements 
  • Dynamics

Density Matrices: 

  • Pure versus mixed ensembles
  • Quantum Statistical Mechanics
  • Thermal Entropy


  • Reduced Density Matrix
  • Schmidt Decomposition
  • Entanglement entropy and Non-locality
  • Local Measurements and disentangling

Quantum "Paradoxes": 

  • Bell's Inequality
  • Schrodinger's Cat
  • No-clone Theorem

Quantum Computing: 

  • Quantum Information, Complexity and Parallelism
  • Q-bit formalism
  • Quantum Algorithms - Deutsch algorithm, Grover Algorithm

Symmetry in Quantum Mechanics:

  • Continous symmetries;  Spatial translations, rotations and angular momentum (briefly)  
  • Discrete symmetries; Parity, lattice translations, time-reversal 

Approximation methods:

  • Time Independent Perturbation Theory 



Approximation methods: (cont'd)

  • Time dependent perturbation theory
  • Berry's phase and adiabatic evolution

Scattering Theory

  • Landauer Transport theory for electrical conduction
  • Elastic and Inelastic scattering (dynamical structure factor)

Path Integral Formulation of Quantum Mechanics:

  • Real time and Euclidian path integrals
  • Instantons and tunneling
  • Path integrals for identical particles

Lattice Quantum Field Theory: 

  • Quantum Transverse Field Ising model 
  • 1d Quantum Ising Model and Majorana Fermions

Continuum Quantum Field Theory: 

  • Many Quantum particles: 2nd Quantization for Bosons and Fermions
  • BEC and weakly interacting Bosons
  • Fermi Gas
  • Quantizing the Electro-Magnetic field
  • Dirac model in 1d, 2d and 3d