Physics 215A (Fall 2017)

Physics 215A, Graduate Quantum Mechanics, Fall 2017

 

Prof. Matthew Fisher 

email: mpaf@kitp.ucsb.edu ;
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:  http://www.kitp.ucsb.edu/mpaf

Grader/TA: Kevin Kuns

email: kuns@physics.ucsb.edu  ;
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 set 1

Problem set 2

Problem set 3

 

 

 

(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

Entanglement: 

  • 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

Symmetry in Quantum Mechanics:

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

Approximation methods:

  • WKB (semiclassical) approximation
  • Variational method
  • 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)

Quantum Computing: 

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

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