1. Physics 541 A quantum approach to condensed matter physics

2. Syracuse students - please put homework from all of you in one envelope and mail to me no later than Thursday afternoon. If you are not ready by that time, then mail your homework separately. Mail it to: CWRU students - please put your individual homework in my mail box no later than Thursday afternoon. Prof Philip Taylor Dept of Physics CWRU Cleveland OH 44106-7079

3. Recapitulation of Class 4 Hartree-Fock approximation gives an answer that is worse than if we just ignored interactions!

4. Look for approach that could give plasmons Recapitulation of Class 5 To second order in V

5. Problem: What operator creates plasma oscillations? Quasiparticle excitations vs collective excitations Equation-of-motion approach Can we find an operator like this for the Coulomb gas?

6. Try After lots of work: So this operator is good if q is big, but not if it is small.

7. Can we find an operator like this for the Coulomb gas? doesn’t work Try the density fluctuation operatorWe know that so we just sum this over all p Interaction terms cancel, so still no good!

8. Remember that plasmon energy squared is linear in the coupling Could it be that

9. Let’s miss out a few steps and go to the result -- becomes is really special!

10. For small q is really special!

11. What is happening? Screening! Small q -- screening possible. Plasmons are relevant excitations Large q -- screening impossible. Quasiparticles are relevant excitations Can this be related to the concept of a dielectric constant?

12. with Terms linear in U can be written as

13. Look at a sample term in U eff