Link to pdf file for slides

1. The goals of the course (as stated on the final slide of Lecture 1: Understanding of the role of electrons in condensed matter
   • Practical, useful knowledge of methods that are working tools of theorists, experimentalists, and researchers in many fields
     Without the burden of heavy math, many-body theory
   • Appreciation for the real many-body problems presented by electrons in condensed matter
     Understanding when to expect correlation to be important
     The grand challenges of condensed matter physics today
   • In extra special lectures a very brief introduction to:
     Practical, useful knowledge of many-body methods that are becoming more and more important for quantitative predictions and understanding the grand challenges in condensed matter
2. Did we meet the goals?
   • All the topics of a book on solid state physics is "electronic structure" -- papers on electronic structure calculate structures, stress-strain relations, magnetism phonons, . . .
   • The electronic structure problem is a HARD problem - among the most exciting, important problems in physics
     • Many-body interacting electrons present the most interesting phenomena in our world
     • Must have very accurate solutions to be useful
   • The advance of Hohenberg, Kohn, and Sham was a major step for approaching many body problems that has provided a new - useful - approach to interacting \electrons
   • Methods for calculations have made major advances
     • The Car-Parrrinello method changed the field and made possible calculations not dreamed of before
     • the plane wave pseudopotential method with iterative algorithms and FFTs is extremely efficient and provides a way to approach MANY problems
     • MANY Examples - difficult calculations -- that can be understood in terms of the important ideas
     • CRUCIAL to be aware of the problems and failures - most of all the failures for excitation energies
3. Topics NOT covered - short listening in the projected slides - discussion in class
   • Magnetism
     • The useful models and the conceptual problems - can describe as localized spins or as bands - the challenge is to understand the relation between these approaches
   • Wannier functions – transformation from extended Bloch states to localized orbitals
     • Show the basic of LCAO and connections to other approaches
     • Very useful for understanding and interpreting properties of electrons in solids
     • Provides a way to think about the issues in magnetism
   • Order-N methods
     • Why do calculations scale as a power (or even exponentially in the number of electrons? Is it possible to have methods that scale as N?
     • Ideas of "nearsightedness" - approaches based on Wannier-like functions - possible but not very useful so far
   • Electric polarization in solids – using Wannier functions (or Berry phases) -- NOT DISCUSSED IN CLASS
   • Excitations and time dependent density functional theory -- ONLY MENTONED BRIEFLY IN CLASS