1. Course up to now
   • Single Body problems in quantum mechanics
   • Self-consistent field approaches to many-body problems
   • Density functional theory for many-electron systems
   • Quantum states in periodic systems
   • Solution by matrix diagonalization, e.g., plane wave calculations
   • Time-dependent Schrodinger Eq. and Iterative methods
     • Real Time
     • Imaginary Time
   • Solution by iterative methods
2. Remainder of Course
   • Next Lecture: Start Many-Body Problems in Quantum Mechanics
   • Emphasize again the importance of projects
   • Not as much homework (one more on Monte Carlo Methods)
   • Further discussion of Iterative methods
     Lanczos algorithm is the key method of "exact diagonalization" in many-body problems
3. Status of Current computational methods using density functional theory
   • Examples of important successes: silicon, carbon, ....
4. Examples of Iterative methods and Car-Parrinello simulations
   • Original Car-Parrinello calculation on Si
   • Large scale calculation: Melting of Carbon
   • Surfaces
   • Quantum dots with 100's - 1000's of atoms

Next time:
Many-Body problems - Introduction to remainder of course