**Fall 2013**

__Instructor__

Dept. of Electrical Engineering,
University of Notre Dame

Office: Fitz 271

__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__

__Grading__

70% Assignments

10% MidTerm

20% Final

__Contact__

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