EE 80687: Advanced Quantum Mechanics

Fall 2013

 

Instructor

Debdeep Jena

Dept. of Electrical Engineering, University of Notre Dame

Office: Fitz 271

Web: http://www.nd.edu/~djena

 

Class Hours

Fall 2013 – Mondays and Wednesdays  (+ a few makeup classes on Fridays).

9:30 am – 10:45 am, DBRT 331.

Office hours: TBD.

 

Prerequisites

Solid-State (or Semiconductor) Physics, and Quantum Mechanics.

 

Objectives

This course on advanced quantum mechanics will begin with a review of basic quantum mechanics and exactly solvable problems.  The Dirac operator formalism will be developed and used for perturbation theory.  Perturbation theory will be applied to light-matter interaction and transport problems ranging from drift-diffusion, tunneling, and ballistic transport.  Green's function approaches will be introduced to understand open quantum systems, and in particular semiconductor devices.  Going beyond the perturbation picture, field quantization and Feynman diagram approaches will be described for semiconductor phenomena involving phonons, excitons, polarons, polaritons, and similar field excitations.  Electron-electron interaction effects, and metal-insulator transitions will be discussed as many-body problems.  The course will end with a study of the increasingly important and relevant geometrical and topological aspects of semiconductor physics.  The topics covered will be the manifestation of the geometric Berry phase in polar semiconductors, to Chern numbers and the quantum Hall effects.  The natural extension to topological insulators, and the recent interest in Majorana Fermions will round off the course.

 

Topics [Reading]

 

1) Review of basic quantum mechanics [Born’s Nobel Lecture, Wilczek on Electrons, your fav QM text…]

2) Exactly solvable problems [Your old fav QM texts, and the QM text references below]

3) Perturbation theory [Class notes + Kroemer, Sakurai]

4) Light-matter interaction [Kroemer, Sakurai]

5) Transport and tunneling  [Notes]

6) Perturbation to higher orders: Feynman diagrams and Kubo formalism  [Notes]

7) Green's function approach for electron conductivity [Notes, Datta NEGF chapters]

8) Field-quantization: Phonons, Polarons, Photons, Excitons, Polaritons and other field excitations [Kroemer]

9) Many particle quantum mechanics: Electron-electron interactions, and metal-insulator transitions [Kroemer]

10) Geometrical and topological quantum mechanics: Berry phases and Chern numbers [RMP review]

11) Quantum Hall effects, Topological insulators, and Majorana Fermions [RMP review]

12) The Dirac equation [Sakurai, Shankar]

 

References

 

1) Notes [Warning: The notes are VERY incomplete and are a work in progress (and that is an understatement).  Use them with that in mind!]

2) Handouts

3) Sections/chapters from

-Sakurai (Modern Quantum Mechanics),

-Shankar (Principles of Quantum Mechanics), and

-Kroemer (Quantum Mechanics).

 

Supporting Slides

Slides (pdf)

 

Supporting Illustrations (Mathematica)

File (*.nb) Note: Right click and save on your computer first to use it.

 

Assignments

1 - pdf  posted:09/03/2013       due: 09/13/2013                       solutions

2 - pdf  posted:09/16/2013       due: 10/01/2013                       solutions

3 - pdf  posted:10/03/2013       due: 10/14/2013                       solutions

4 - pdf  posted:10/19/2013       due: 10/30/2013                       solutions

5 - pdf  posted:11/12/2013       due: 11/26/2013                       solutions

6 - pdf  posted:12/02/2013       due: 12/19/2013                       solutions

 

Exams

MidTerm

Final

 

Grading

70% Assignments

10% MidTerm

20% Final

 

Contact

Email: djena at nd dot edu if you have any questions.