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Last updated 2025-May_29

Physics 5400: Quantum Theory of Many-Particle Systems, Fall 2025

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 26. 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 starting August 29. If this time presents a scheduling problem, we can arrange a different time.

Instructor: Willem Dickhoff
Office: Compton 371; Email: wimd@wustl.edu
Office hours: F 10:00-11:00 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 a reduced price). A 3rd edition is in press with an additional 130 pages covering recent progress. Publication date probably during the Fall semester.
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.  Much of the material covered in the first 5 chapters was discussed in Phys 524 last Spring. We will therefore only very briefly review the topics. Arrangements can be made to prepare for the course by going over the topics covered in 524 if necessary.

Lecture
Subject material meeting date Hwk for weekly meeting Presentation
#1 Chapter 1&2 discussion & review Identical particles & Second Quantization 8/26/2025 Work out details arriving at Eq. (2.41) and (2.46)
#2 Chapter 3 discussion & review IPM for fermions in finite systems review 8/28/2025 Review numerical solution of eigenvalues for neutrons in 208-Pb or electrons in He, Ne, Ar using effective potential. (Material from 523-24)

#3 Prerequisites
Discussion of QM preparation 8/29/2025 Discussion of problems
#4
Chapter 4 discussion and review Two-particle states & Interactions 9/2/2025 Review Ch.4.1-4. Calculate 4.7 as preparation for later numerical work. Optional 4.5 for nuclear focus.
#5 Chapter 5 review Electron gas and matter of nuclei; Bosons and BEC 9/4/2025 Ch.5.1 (due 9/5) --> see details in Fetter&Walecka
Band problem (due 9/12) for electron focus.

#6 Electrons in lattice environment
Focus discussion 9/5/2025 Discussion of problems
#7 Chapter 6.1-3 Propagators in one-particle quantum mechanics 9/9/2025 Ch.6.1-2 and 6.3 optional.

#8 Chapter 6.4-5 Propagators and scattering 9/11/2025 Ch.6.4 and 6.5 nuclear focus. Review of Numerov.

#9 Chapter 6
Homework issues 9/12/2025 Discussion of problems
#10 Chapter 7.1-7.4 App. A SP propagator in the many-body system; 9/16/2025
Review QM pictures: Heisenberg and Interaction.


#11
Chapter 7.5-7.8 Discussion of related experimental data 9/18/2025 Read (e,2e) paper (E) or (e,e'p) paper (N)
#12 Chapter 7
Homework issues 9/19/2025 Discussion of problems
#13 Ch.8.1-3 Interaction picture etc.
Perturbation expansion single-particle propagator
9/23/2025 Ch.8.1-2
Optional: Wick's theorem

#14 Chapter 8.4-6 Diagrams & rules; Diagrams energy; 9/25/2025 Ch.8.4
#15 Chapter 8 Homework issues 9/26/2025 Discussion of problems
#16
Chapter 9.1-3
Dyson equation; Equation of motion method 9/30/2025
Ch.9.1
#17 Chapter 9.4-5 Two-particle propagator; Self-energy, vertex function & Dyson equation 10/2/2025 Ch.6.3
#18 Chapter 9 Homework issues 10/3/2025 Discussion of problems



10/7/2025 No class Fall Break
#19 Chapter 10.1-2 Hartree-Fock 10/9/2025 NUMERICAL Neon atom Hartree-Fock after doing He first
#20 Chapter 10 Homework issues 10/10/2025 NUMERICAL issues

#21 Chapter 10.4-5 Hartree-Fock in infinite systems 10/14/2025 Pick E or N HF option
#22 Chapter 11.1-2 & 5 Beyond HF in finite systems 10/16/2025 Numerical solution with E-dependent self-energy

#23 Chapter 11 Homework issues 10/17/2025 Presentation topic
#24
Chapter 11.3-4 Beyond HF in infinite systems 10/21/2025

#25 Chapter 12.1-3 Bose systems; Hartree-Bose 10/23/2025

#26 Chapter 12 Homework issues 10/24/2025

#27 Chapter 12.4 GP equation; scattering theory 10/28/2025 Topic of presentation
#28 Chapter 13.1-5
Excited states; Random Phase Approximation 10/30/2025

#29 Chapter 13 Outlook discussion
10/31/2025

#30 Chapter 14.1-3 Excited states infinite systems; Lindhard function; Plasmons 11/4/2025

#31 Chapter 15.1-3 pphh Propagator; Cooper and pphh eigenvalue problem; Gap and pairing instability 11/6/2025

#32 Chapters 14 & 15
Outlook discussion
11/7/2025

#33 Chapter 16.1-4 Self-energy infinite system & electron gas; GW 11/11/2025

#34 Chapters 16,22 Nuclear matter & saturation, pairing intro 11/13/2025

#35 Chapters 16 & 22 Outlook discussion
11/14/2025

#36 Chapter 17, 18 Finite nuclei and atoms; Bosons; anomalous propagators 11/18/2025

#37 Chapter 18, 22 Bosons; anomalous propagators; Pairing intro 11/20/2025

#38 Chapter 22 Anomalous propagators; gap equation 11/21/2025

#39 Chapter 21 Conserving approximations 11/25/2025


Thanksgiving Break
11/26-11/30

#40 Chapter 24 Finite temperature I 12/2/2025

#41 Chapter 24 Finite temperature II 12/4/2025

#42 Chapter 24 Finite temperature III 12/5/2025


Presentations
12/11/2025 10 AM-1 PM Compton 241


Presentations
12/12/2025 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. Part of classes may be presented by students using provided slides that cover the material.

FORMAT OF COURSE:

  1. Three meetings per week in Crow 206 (TTh) and Compton 245 (F)
  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 pdf/keynote/powerpoint is recommended
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.