Electronic Structure of Condensed Matter:    Course Syllabus
Physics 498CQM/CSE 498  - Spring 1999
Instructor: 
           Richard Martin
               Professor of Physics UIUC
               rmartin@uiuc.edu 
               1-217-333-4229
               301A Loomis		 Graders:
             William Mattson          Tim Wilkens
             Graduate Student                 Graduate Student
              wmattson@uiuc.edu            wilkens@uiuc.edu
             1-217-244-0391                   1-217-333-1686
             390Y  Loomis                       390H Loomis
Class Time and Location: 3:30 - 4:50 M W 158 Loomis Laboratory

         Click here to go the Course Home Page

(March 31, 1999 - May be modified further during semester)

Date 
# 
Lecture Topic 
Notes 
Hmwk
1/20
1
 Introduction to Electronic Structure
-
-
Independent Particle Approximation and Density Functional Theory
1/25 
2
 Theoretical Background: General Conclusions; Independent Particle Approximation (Hartree; Hartree-Fock; Density Matrices)
- 
1
1/27 
3
 Crystal Symmetry and Bloch States
- 
-
2/1 
4
 Basic Understanding of Bands in Solids: Empirical Tight-binding
- 
-
2/3 
5
 Density Functional Theory: Theorems; Kohn-Sham Theory; LDA
- 
2
2/8 
6
 Density Functional Theory: Beyond the LDA: GGAs; nonlocal functionals -- Applications of DFT to Atoms
- 
-
2/10 
7
 Pseudopotentials: Theory and Practice
- 
-
2/15 
8
 Plane Wave Calculations in Crystals; Empirical Pseudopotentials
- 
-
2/17 
9
 Plane Wave Calculations in Crystals; self consistent DFT
- 
-
2/22 
10
 Atom Centered Orbital Bases: LCAO; Start Muffin Tin Based Methods
- 
-
2/24 
11
 Continue Muffin Tin based methods: APW; LAPW; LMTO; KKR
- 
3
 
11a
 Introductory notes:  Prototype problems: Jellium; Kondo/Anderson; Hubbard
- 
-
Interacting Electrons - Exchange and Correlation 
3/1 
12
 Lectures by Prof. D. Ceperley:  Monte Carlo Methods - Variational Monte Carlo
- 
-
3/3 
13
 Beyond Variational Monte Carlo  -  Diffusion, Path Integral?  to be decided
- 
-
3/8 
14
 Beyond Variational Monte Carlo  -  Diffusion, Path Integral? to be decided
- 
-
3/10 
15
 Quantum Monte Carlo on Lattices
- 
4
3/18-24 
- 
 No Lectures: Spring Break and APS Meeting 
- 
-
3/29 
16
 Excitations of the many-electron system: Fermi Liquid Theory; Random phase approximation; and Quasiparticles 
- 
-
3/31 
17
 Green's Functions, Self-energies; Quasiparticles; Luttinger Theorem on Fermi Surface
- 
5
4/5 
18
 Kondo/Anderson and Hubbard; Large N and Large D limits; Heavy Fermions
- 
-
4/7 
19
 "GW" Calculations in solids - resulting quasiparticle bands 
- 
-
Advanced Methods using DFT and Independent Particle Approaches
4/12 
20
 Iterative methods in solving independent-particle equations
- 
-
4/14 
21
 Iterative methods continued: Plane Waves; Grid-based Finite Difference Eqs.
- 
-
4/19 
22
 "Ab Initio" Molecular Dynamics (Car-Parrinello-type methods)
- 
-
4/21 
23
 Linear Response Theory: Phonons; "2n+1 theorem"
- 
-
4/26 
24
 Electric Polarization in Solids: Berry's phases and Wannier Functions
- 
-
4/28 
25
 Linear Scaling O(N) Methods for Electronic Structure
- 
-
Strongly-Correlated Electrons
5/3 
26
 Strongly Correlated Systems: Metal Insulator Transitons; Collosal Magnetoresistance
- 
-
5/5 
27
 Hi-Tc Superconductors - Conclusions
- 
-
5/10 
FINAL EXAM WEEK - Project Reports

Send reports of problems to TAs:
William Mattson, wmattson@uiuc.edu and Tim Wilkens, wilkens@uiuc.edu
Click here to go the Course Home Page