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Last updated 2021-Oct_6

Physics 540: Quantum Theory of Many-Particle Systems, Fall 2021

There will be no Final Exam for this course.


The course meets on Tuesday, Thursday, from 11:30-12:50 pm in Crow 206. First class is on Tuesday, August 31. 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 is Friday 1:45-2:35 pm in Compton 245 starting September 3.

Instructor: Willem Dickhoff
Office: Compton 371; Email:
Office hours: We 11:30-12:30 on Zoom and appointment


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 in the library are:
Fetter and Walecka
Abrikosov, Gorkov, and Dzyaloshinski
Negele and Orland
Blaizot and Ripka
Kadanoff and Baym
Pitaevskii and Stringari
Nozieres and Pines
Koltun and Eisenberg
Kraeft et al.
Lindgren and Morrison
Bruus and Flensberg
Altland and Simons
Cohen-Tannoudji and Guery-Odelin
Stefanucci and van Leeuwen
(on reserve in the physics library)

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. We will try to insert some new formats into the course. I propose to provide the lecture material for each class a week ahead of schedule. After agreeing on a presentation schedule a student will then have a week to prepare to present this material while having full access to feedback and further clarification from the instructor. The hope is that students will be better able to absorb and apply the considerable amount of material that is covered in the course. It also provides an opportunity to practice the critical skill of presenting and perhaps the skill of asking questions.

Subject material meeting date Hwk Presentation
#1 Chapter 1.1-4 Identical particles 8/31/2021 1-1 (due 9/3) only for N=2
#2 Chapter 1.5 & 2 Identical particles & Second quantization 9/2/2021 2-1 (one example), 5 & 6 (due 9/3)
#3 Prerequisites
Chapters 1-2
Discussion of QM preparation 9/3/2021 Discussion of problems
Chapter 3 IPM for fermions in finite systems 9/7/2021 Numerical solution of eigenvalues for neutrons in 208-Pb or electrons in He, Ne, Ar using effective potential (due 9/24).
#5 Chapter 3 IPM Atoms & Nuclei
9/9/2021 Ch.4.1-4 (9/10 or 9/17) (4.7 is for later numerical work) Numerical Work (due 9/17)

Numerical preparation? 9/10/2021 Discussion of problems Liam, Yueheng, Tekeba
#7 Chapter 4.1-4 Numerical determination of eigenvalues etc.
Nuclei; Two-particle states; Interactions; Fermi gas
9/14/2021 Numerical work

#8 Chapter 5.1-4 Electron gas and more 9/16/2021 Ch.5.1 (due 9/24) -->Fetter & Walecka
Band problem (due 9/24)

#9 Chapters 3 & 4 Homework issues 9/17/2021 Discussion of problems (numerics?) JR
#10 Chapter 5.5-6
Bosons and BEC 9/21/2021

Chapter 6.1-3
Propagators in one-particle quantum mechanics 9/23/2021 Ch.6.2 (due 10/15)

#12 Chapters 5 Homework issues 9/24/2021 Discussion of problems Mary
#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 9/28/2021 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. 9/30/2021

#15 Chapter 6,7 Homework issues 10/1/2021 Discussion of problems Haonan

Finish numerical problem 10/5-8/21 during office hour or by appointment
#16 Chapter 8.4-6 Perturbation expansion single-particle propagator; Wick's theorem optional 10/5/2021 Ch.8.1-2 (due 10/15)
#17 Chapter 8.5-6; start Chapter 9.1-3 Diagrams & rules; Diagrams energy; Equation of motion method 10/7/2021 Ch.8.4 (due 10/15)

#18 No meeting

10/8/2021 Faculty meeting

Fall Break
10/12/2021 No class
#19 Chapter 9.4-5; Chapter 10.1-2 Two-particle propagator; Self-energy, vertex function & Dyson equation; Hartree-Fock 10/14/2021 Ch.9.1 (due 10/15 and Ch.6.3 (due 10/15)
#20 Chapter 10
Homework issues 10/15/2021 Discussion of problems; presentation of numerical work Mehrnoosh (5.1)
#21 Chapter 10.4-5 Hartree-Fock in atoms & infinite systems 10/19/2021 NUMERICAL Neon atom Hartree-Fock after doing He first
#22 Chapter 11.1-2 & 5 Beyond HF in finite systems 10/21/2021

#23 Chapter 11
Homework issues 10/22/2021 Discussion of problems
Chapter 11.3-4 Beyond HF in infinite systems 10/26/2021

#25 Chapter 12.1-3
Chapter 13 start
Bose systems; Hartree-Bose 10/28/2021

#26 Chapter 12
Homework issues 10/29/2021 Discussion of problems; topic of presentation
#27 Chapter 12.4
Chapter 13 continued
GP equation; scattering theory 11/2/2021 Ch.13.1 (11/15 optional); Ch.13.2 (due 11/22) NUMERICAL (optional)
#28 Chapter 13 finished
Chapter 14.1-3
Excited states infinite systems; Lindhard function; Plasmons 11/4/2021

#29 Chapter 13
Homework issues 11/5/2021 Topic of presentation ("due" 11/1)
#30 Chapter 15.1-3 pphh Propagator; Cooper and pphh eigenvalue problem; Gap and pairing instability 11/9/2021 Ch.15.7 (due 11/22) NUMERICAL (optional)
#31 Chapter 16.1-4 Self-energy infinite system & electron gas; GW 11/11/2021

#32 Chapters 14-16 Homework issues 11/12/2021 Discussion of problems
#33 Chapter 16.22 Nuclear matter & saturation, pairing intro 11/16/2021

#34 Chapter 17, 21, 18 Finite nuclei and atoms; Bosons; anomalous propagators 11/18/2021

#35 Chapter 17
Homework issues 11/19/2021 Discussion of problems
#36 Chapter 18, 22 Bosons; anomalous propagators; Pairing intro 11/23/2021

Thanksgiving Break

#37 Chapter 22 Anomalous propagators; gap equation 11/30/2021

#38 Chapter 24 Finite temperature I 12/2/2021

#39 Chapter 22,24 Homework issues 12/3/2021

#40 Chapter 24 Finite temperature II 12/7/2021

#41 Chapter 24 Finite temperature III 12/9/2021

Chapter 22,24 Homework issues

12/16/2021 11:30AM-1:30PM Compton/Crow

12/17/2021 1-4PM Compton/Crow

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.


  1. Three meetings per week in Crow 206 and 223
  2. Reading for each class. Homework assigned for most class. 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. To encourage classroom participation students will rotate in presenting class material which is part of the final grade.
  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
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:


Course Evaluation

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