Quantum Theory of Many-Particle Systems

MWF 10:00 - 11:00 pm, Compton 245

Wim Dickhoff

Fall 2000

- Textbook: No textbook required

**Quantum Theory of
Many-Particle Systems**

Physics 540, Fall 2000 Tentative Schedule August 30, 2000

Instructor: Wim Dickhoff

Textbook: Fetter & Walecka (very, very optional: sticker price $140 in the bookstore)

The outline below is still very tentative for classes later in the Semester. Reading assignments should be taken very seriously. The reading of handout pages is required. Other references to various books are optional reading but recommended to get a broader perspective. The table below should be read as follows: the third row of the table in the column under reading assignment refers to the reading of handout pages 3-9. These should be read before the first meeting of the class. The plan is to distribute the handout pages by e-mail in the form of a postscript file which can be printed on a favorite printer.

Handout
p.1-2 Course
rules Sakurai Ch.
6.1-2 Getting
acquainted; what's the plan; course rules Identical
particles; (Anti)-Symmetric two-body and many-body states;
Fermion and boson scattering Second
quantization; Occupation number representation;Fock space;
Operators LABOR DAY;
NO CLASS Sakurai Ch.
3.7 Independent
particle model; Atoms; Nuclei; FW Ch.
1.3 Isospin;
Fermi gases: Electron gas, Nuclear/neutron matter,
Interactions;
Examples of two-body interactions FW Ch.
2.4-5 Phys. Today
12/99 Statistical
mechanics; Ideal gas;Bosons at finite temperature;
Bose-Einstein condensation Trapped
bosons at finite temperature; Fermions at finite
temperature; Fermion degeneracy in traps Sakurai Adv
QM Koltun
Eisenberg Ch. 3 Quantization
of the electromagnetic Field; Maxwell's equations ; Free
field solutions; Photons and many-photon states Sakurai Adv
QM Koltun
Eisenberg Ch. 3 Interaction
of electrons with the EM-field; Emission and absorption of
photons by atoms; Blackbody radiation; Laser
principle Sakurai Ch.
2.5 Single-particle
propagator in one-particle QM; Time-evolution; Eigenvalue
problems; Diagrams Scattering
theory and propagators; Partial waves and phase
shifts Sakurai Ch.
2.1-2&5.6 Time-evolution;
Pictures Schrödinger / Heisenberg / Interaction;
FW Ch.
3.6 Adiabatic
turning on of the interaction; Gell-Mann and Low
theorem FW Ch.
3.7 Single-particle
propagator in a many-aprticle system; Spectral
functions Single-particle
propagator in the independent particle model; Comparison
with experimental results: e,2e; e,e'p Wick's
theorem; diagrams Analysis of
perturbation theory Self-energy;
Equation of motion method Handout Hartree-Fock;
infinite system Atoms Atoms
(nuclei) Beyond
Hartree-Fock ; Second order FALL BREAK;
NO CLASS Dynamic
structure function (weak probe); Excited
states; separable interaction & finite system Lindhard
function; Plasmons (data including atoms) Zero sound
(data); Landau parameters Results for
electrons (GW) and nuclei Brueckner
Ladder diagrams; Galitski development; scattering in free
space; Scattering length Scattering
of dressed particles Results
including second order; effective mass History and
present status; Healing argument PP RPA
finite nuclei; instability Pairing in
nuclei Cooper
problem; instability; eigenvalues Superconductivity;
superfluidity of More
formalism; neutron stars Finite
temperature I Thanksgiving
Recess; NO CLASS Thanksgiving
Recess; NO CLASS Finite
temperature II Finite
temperature III Transport Applications;
connection with field theory Compton
profile; density matrices Bose
condensate; Gross-Pitaevski Lambda-transition;
superfluidity Quantum and
fractional quantum Hall effect

^{3}He liquid; Symmetry considerations for two
particles
^{3}He; d-waves
^{4}He

1. FORMAT OF COURSE:

i. Three lectures per week on Monday, Wednesday, and Friday from 10-11am in Compton 245ii. One hour review/discussion meeting a week where problems are presented by the students

iii. About one problem per class to be discussed during the discussion meeting

iv. A few computer assignments

v. No exams

vi. A paper discussing the material of a relevant set of articles from the literature related to the material of the course is to be turned in before the last class. This paper must be written in revtex format (used in Physical Review journals) and should contain a proper set of references. Using the documentstyle [pra,aps] the paper should be at least 7 but not more than 10 pages long and may include equations but not detailed derivations (if necessary they can be included in an appendix). Half a page containing a proposal for the topic of the paper is due during the last class before Fall break.

vii. A 30-minute presentation on the material of the paper is required. Attendance at all talks by other students is also required. This talk should include a motivation, a discussion of the method of solution and experimental data (where appropriate), a discussion of the results, and a summary plus conclusions of the presented material. The use of overhead transparencies is recommended.

viii. Classroom participation and discussion is mandatory.

ix. Reading assignments should be completed before the next class.

2. GRADING POLICY:

- Homework problems 20%
- Computer assignments 20%
- Paper 20%
- Presentation 20%
- Reading assignments 10%
- Everything else including class participation 10%

**You can download the course
schedule and information from the regular
website**** ****Acrobat
Reader****.**

- Tentative Course Schedule
- Handout section #1
- Handout section #2
- Handout section #3
- Handout section #4
- Handout section #5
- Handout section #6
- Handout section #7
- Handout section #8
- Handout section #9
- Problem #1
- Problem #2
- Problem #3
- Problem #4
- Problem #5
- Problems #6,7,and 8
- Problems #9 and 10
- Problem #11
- Problems #12 and 13
- Problems #14 and 15
- Problem #16
- Problems #17 and 18
- Problem #19
- Problems #20 to 23