Physics 215A (Fall 2017)

Physics 215A, Graduate Quantum Mechanics, Fall 2017


Prof. Matthew Fisher 

email: ;
Office: 2305 Kohn Hall
Lectures: Tuesday, Thursday 11:00-12:15 pm, Phelps 1508
Office Hours: Tuesday  2:00-3:30 pm

Find the course web site thru my personal web site:

Grader/TA: Kevin Kuns

email:  ;
Office Hours: Friday 1:30-4:30pm  Broida 6228


Textbooks: The "official" textbook for 215A is Sakurai/Napolitano (2nd edition), which is a good book covering many traditional topics.   And of course there are a number of other such books - including Shankar, Gottfried/Yan, Landau-Lifshitz, among others.  However, I am hoping to include some more modern topics (eg entanglement entropy, quantum computing) which are not in these books.  I will try to suggest other reading/books when relevant.

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

Exams:  Perhaps a Take-Home final.


Help/feedback:  In addition to my office hours and Kevins' 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.  


Quantum mechanics is a truly remarkable field.  Hopefully we can all develop a conceptual intuition for the topic (perhaps dispensing with some of the math, early on?), and have some fun along the way!


Problem Sets


Problem Solutions





(Tentative) SYLLABUS for 215A (and 215B)

Mathematical Primer:

  • Linerar vector spaces, dual spaces, Dirac notation and operators 
  • Eigenvectors/eigenvalues of Hermitian operators
  • Projection and Completeness
  • Unitary Transformation and Representations
  • Compatible and Incompatible Operators

Formulation of Quantum Mechanics:

  • U-Process:  Dynamics, Unitary Time Evolution and the Hamiltonian Operator
  • R-Process: Measurements and State Reduction

2-State Quantum System(s):

  • Measurements 
  • Dynamics

Density Matrices: 

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


  • Reduced Density Matrix
  • Schmidt Decmposition
  • 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   
  • Discrete symmetries; Parity, lattice translations, time-reversal 

Approximation methods:

  • Variational method
  • WKB (semiclassical) approximation
  • Time Independent Perturbation Theory
  • 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

Quantum Particles: 

  • Single Quantum particle - tight binding model, translational symmetry and the continuum limit
  • Many Quantum particles: 2nd Quantization for Bosons and Fermions
  • Lattice Quantum Field Theories