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Last updated 2023-Aug_30

Physics 540: Quantum Theory of Many-Particle Systems, Fall 2023

There will be no Final Exam for this course.

Teaching

The course meets on Tuesday, Thursday, from 11:30-12:50 pm in Crow 206. First class is on Tuesday, August 29. Additional meeting time is scheduled to analyze and discuss homework, allow for student presentations and the possibility of make-up classes, if needed. Time for this meeting will be on Fridays from 11-11:50 in Compton 245.

Instructor: Willem Dickhoff
Office: Compton 371; Email: wimd@wuphys.wustl.edu
Office hours: We 11:30-12:30 on Zoom and appointment

Books

Course Textbook: Many-body theory exposed! (2nd edition) by Dickhoff and Van Neck, ISBN 9812813802 (softcover; note there is also a hardcover that is some times offered at reduced price).
We will cover a substantial fraction of the material in the book. Additional reading, references, and homework problems can be found there as well.
Other useful books: Additional books that you should consult once in a while:
Mattuck
Fetter and Walecka
Abrikosov, Gorkov, and Dzyaloshinski
Negele and Orland
Blaizot and Ripka
Migdal
Mahan
Kadanoff and Baym
Schrieffer
Thouless
Pitaevskii and Stringari
Nozieres
Nozieres and Pines
Koltun and Eisenberg
Kraeft et al.
Lindgren and Morrison
Brown
Bruus and Flensberg
Altland and Simons
Cohen-Tannoudji and Guery-Odelin
Leggett
Stefanucci and van Leeuwen

Course outline

The course is defined by the material discussed in the lectures and studied in the reading material. A tentative schedule is given below. It includes the material to be read for the corresponding meeting, the material covered, and the assigned homework. Some people have seen the initial material in Phys 524.

Lecture
Subject material meeting date Hwk for weekly meeting Presentation
#1 Chapter 1.1-4 Identical particles 8/29/2023 1-1 (due 9/1) only for N=2
#2 Chapter 1.5 & 2 Identical particles & Second quantization 8/31/2023 2-1 (one example), 5 & 6 (due 9/8)
#3 Prerequisites
Chapters 1-2		 Discussion of QM preparation 9/1/2023 Discussion of problems
#4
 Chapter 3 IPM for fermions in finite systems 9/5/2023 Numerical solution of eigenvalues for neutrons in 208-Pb or electrons in He, Ne, Ar using effective potential (due TBA).
#5 Chapter 3 IPM Atoms & Nuclei
 9/7/2023 Ch.4.1-4 (9/15 or 9/22) (4.7 is for later numerical work) Numerical Work (due 9/29*)
#6
Numerical preparation? 9/8/2023 Discussion of problems
#7 Chapter 4.1-4 Numerical determination of eigenvalues etc.
Nuclei; Two-particle states; Interactions; Fermi gas 		9/12/2023 Numerical work
#8 Chapter 5.1-4 Electron gas and more 9/14/2023 Ch.5.1 (due 9/22) -->Fetter & Walecka
Band problem (due 9/29*)
#9 Chapters 3 & 4 Homework issues 9/15/2023 Discussion of problems (numerics?)
#10 Chapter 5.5-6
 Bosons and BEC 9/19/2023

#11
 Chapter 6.1-3
 Propagators in one-particle quantum mechanics 9/21/2023 Ch.6.2 (due 10/20)
#12 Chapters 5 Homework issues 9/22/2023 Discussion of problems
#13 Chapter 7.1-7.4 App. A
Chapter 7.5-7.7		 SP propagator in the many-body system; Discussion of related experimental data 9/26/2023 Optional:
Read (e,2e) paper or (e,e'p) paper
#14 Chapter 7.8, Ch.8.1-3 (e,e'p) and nuclei; Interaction picture etc. 9/28/2023



Hiatus includes Fall Break


#15 Chapter 8.4-6 Perturbation expansion single-particle propagator; Wick's theorem optional 10/17/2023 Ch.8.1-2 (due 10/20)
#16 Chapter 8.5-6; start Chapter 9.1-3 Diagrams & rules; Diagrams energy; Equation of motion method 10/19/2023 Ch.8.4 (due 10/27)

#17 Chapter 6,7,8,9 Homework issues 10/20/2023 Discussion of problems
#18 Chapter 9.4-5; Chapter 10.1-2 Two-particle propagator; Self-energy, vertex function & Dyson equation; Hartree-Fock 10/24/2023 Ch.9.1 (due 10/27) and Ch.6.3 (due 10./27)
#19 Chapter 10.4-5 Hartree-Fock in atoms & infinite systems 10/26/2023 NUMERICAL Neon atom Hartree-Fock after doing He first
#20 Chapter 11.1-2 & 5 Beyond HF in finite systems 10/27/2023

#21
 Chapter 11.3-4 Beyond HF in infinite systems 10/31/2023

#22 Chapter 12.1-3
Chapter 13 start		 Bose systems; Hartree-Bose 11/2/2023

#23 Chapter 12.4
Chapter 13 continued 		GP equation; scattering theory 11/3/2023 Topic of presentation
#24 Chapter 13 finished
Chapter 14.1-3		 Excited states infinite systems; Lindhard function; Plasmons 11/7/2023

#25 Chapter 15.1-3 pphh Propagator; Cooper and pphh eigenvalue problem; Gap and pairing instability 11/9/2023

#26 Chapter 16.1-4 Self-energy infinite system & electron gas; GW 11/10/2023

#27 Chapters 16,22 Nuclear matter & saturation, pairing intro 11/14/2023

#28 Chapter 17, 21, 18 Finite nuclei and atoms; Bosons; anomalous propagators 11/16/2023

#29 Chapter 18, 22 Bosons; anomalous propagators; Pairing intro 11/17/2023

#30 Chapter 22 Anomalous propagators; gap equation 11/21/2023


Thanksgiving Break
11/22-11/26

#31 Chapter 24 Finite temperature I 11/28/2023

#32 Chapter 24 Finite temperature II 11/30/2023

#33 Chapter 24 Finite temperature III 12/1/2023

#34
 TBA
12/5/2023

#35 TBA
12/7/2023


Presentations
12/14/2023 10 AM-1 PM Compton 241

Presentations
12/15/2023 10 AM-1 PM Compton 241

Grading and format of the course

Course material is completely covered by textbook. To avoid unnecessary duplication, reading material is strongly recommended as study material before class meeting. We review homework as appropriate and should be ready according to the above schedule. A few computer assignments will be part of the course. A presentation on a related topic is required. Class participation is essential for a useful experience. Classes may be presented initially by students using provided slides that cover the material.

FORMAT OF COURSE:

  1. Three meetings per week in Crow 206 and xxx
  2. Reading for each class. Homework assigned for most classes, at least initially. Appropriate review of reading material during class mostly in lecture format (with hopefully discussion and lots of questions). Homework can be discussed during class time and is reviewed when necessary.
  3. Computer assignments as longer projects.
  4. No written exams!
  5. A ~30-minute presentation on material of a closely related topic must be chosen. Attendance at all talks by other students is required. The 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 or (preferably) pdf/keynote/powerpoint is recommended
    6.
COURSE GRADE:
Homework: Students are encouraged to form study groups and discuss the homework with each other, but each student must be able to present his or her own solutions. You will be asked to discuss solution strategies of homework problems when appropriate.

Course materials

Computer assignments:
Slides:

Neutron_levels
Bomo_208Pb_levels


Course Evaluation

During the evaluation period you can supply your evaluation of the course at the course evaluation website.