Physics 540

Quantum Theory of Many-Particle Systems

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

Wim Dickhoff

Fall 2000

 

 


Table of Contents

 

 

 


  • Textbook: No textbook required

 

  • Course Outline

 

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.

 

 

Hwk

 

Mtg#

 

Date

 

Reading Assignment

 

Topics

 

 

 

 

Handout p.1-2

Course rules

 

 

 

1

 

Wed 8/30

 

Handout p.3-9

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

 

1

 

2

 

Fri 9/1

 

Handout p. 10-18

 

Second quantization; Occupation number representation;Fock space; Operators

 

 

 

 

 

 

 

 

Mo 9/4

 

 

LABOR DAY; NO CLASS

 

 

3

 

Wed 9/6

 

Handout p.19-24

Sakurai Ch. 3.7

 

Independent particle model; Atoms; Nuclei;

 

2

 

4

 

Fri 9/8

 

Handout p.24-31

FW Ch. 1.3

 

Isospin; Fermi gases: Electron gas, Nuclear/neutron matter, 3He liquid; Symmetry considerations for two particles

 

 

 

 

 

 

 

5

 

Mon 9/11

 

Handout p.32-36

 

Interactions; Examples of two-body interactions

 

 

6

 

Wed 9/13

 

Handout p.37-41

FW Ch. 2.4-5

Phys. Today 12/99

 

Statistical mechanics; Ideal gas;Bosons at finite temperature; Bose-Einstein condensation

 

3

 

7

 

Fri 9/15

 

Handout p.41-45

 

Trapped bosons at finite temperature; Fermions at finite temperature; Fermion degeneracy in traps

 

 

 

 

 

 

 

8

 

Mon 9/18

 

Handout p.46-49

Sakurai Adv QM

Koltun Eisenberg Ch. 3

 

Quantization of the electromagnetic Field; Maxwell's equations ; Free field solutions; Photons and many-photon states

 

 

9

 

Wed 9/20

 

Handout p.49-52

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

 

4

 

10

 

Fri 9/22

 

Handout p. 53-58

Sakurai Ch. 2.5

 

Single-particle propagator in one-particle QM; Time-evolution; Eigenvalue problems; Diagrams

 

 

 

 

 

 

 

11

 

Mon 9/25

 

Handout p. 58-62

 

Scattering theory and propagators; Partial waves and phase shifts

 

 

12

 

Wed 9/27

 

Handout p.63-67

Sakurai Ch. 2.1-2&5.6

 

Time-evolution; Pictures Schrödinger / Heisenberg / Interaction;

 

5

 

13

 

Fri 9/29

 

Handout p. 67-71

FW Ch. 3.6

 

Adiabatic turning on of the interaction; Gell-Mann and Low theorem

 

 

 

 

 

 

 

14

 

Mon 10/2

 

Handout p. 72-75

FW Ch. 3.7

 

Single-particle propagator in a many-aprticle system; Spectral functions

 

 

15

 

Wed 10/4

 

Handout p. 75-77

 

Single-particle propagator in the independent particle model; Comparison with experimental results: e,2e; e,e'p

 

6

 

16

 

Fri 10/6

 

FW Ch. 3.8-9

 

Wick's theorem; diagrams

 

 

 

 

 

 

 

17

 

Mon 10/9

 

Continue

 

Analysis of perturbation theory

 

 

18

 

Wed 10/11

 

Continue

 

Self-energy; Equation of motion method

 

7

 

19

 

Fri 10/13

 

FW Ch. 4.10

Handout

 

Hartree-Fock; infinite system

Atoms

 

 

 

 

 

 

 

20

 

Mon 10/16

 

Lindgren Morrison

 

Atoms (nuclei)

 

8

 

21

 

Wed 10/18

 

Handout

 

Beyond Hartree-Fock ; Second order

 

 

 

Fri 10/20

 

 

FALL BREAK; NO CLASS

 

 

 

 

 

 

 

22

 

Mon 10/23

 

RPA

 

Dynamic structure function (weak probe);

Excited states; separable interaction & finite system

 

 

23

 

Wed 10/25

 

Electron gas reading

 

Lindhard function; Plasmons (data including atoms)

 

9

 

24

 

Fri 10/27

 

Landau paper

 

Zero sound (data); Landau parameters

 

 

 

 

 

 

 

25

 

Mon 10/30

 

RPA and self-energy

 

Results for electrons (GW) and nuclei

 

 

26

 

Wed 11/1

 

Repulsive core

 

Brueckner Ladder diagrams; Galitski development; scattering in free space; Scattering length

 

10

 

27

 

Fri 11/3

 

Nuclear matter

 

Scattering of dressed particles

 

 

 

 

 

 

 

28

 

Mon 11/6

 

Self-energy BCA

 

Results including second order; effective mass

 

 

29

 

Wed 11/8

 

Nuclear matter

 

History and present status; Healing argument

 

11

 

30

 

Fri 11/10

 

Nuclei

 

PP RPA finite nuclei; instability

Pairing in nuclei

 

 

 

 

 

 

 

31

 

Mon 11/13

 

Pairing infinite matter

 

Cooper problem; instability; eigenvalues

 

 

32

 

Wed 11/15

 

BCS

 

Superconductivity; superfluidity of 3He; d-waves

 

12

 

33

 

Fri 11/17

 

Nambu, Gorkov, Migdal

 

More formalism; neutron stars

 

 

 

 

 

 

 

34

 

Mon 11/20

 

Baym Kadanoff or FW

 

Finite temperature I

 

 

 

Wed 11/22

 

 

Thanksgiving Recess; NO CLASS

 

 

 

Fri 11/24

 

 

Thanksgiving Recess; NO CLASS

 

 

 

 

 

 

 

35

 

Mon 11/27

 

BK or FW

 

Finite temperature II

 

 

36

 

Wed 11/29

 

BK or FW

 

Finite temperature III

 

13

 

37

 

Fri 12/1

 

Baym-Kadanoff

 

Transport

 

 

 

 

 

 

 

38

 

Mon 12/4

 

Baym-Kadanoff

 

Applications; connection with field theory

 

 

39

 

Wed 12/6

 

Gersch-Rodriguez

 

Compton profile; density matrices

 

14

 

40

 

Fri 12/8

 

Momentum distributions

 

Bose condensate; Gross-Pitaevski

 

 

 

 

 

 

 

41

 

Mon 12/11

 

4He

 

Lambda-transition; superfluidity

 

 

42

 

Wed 12/13

 

2D-electrons in magnetic field

 

Quantum and fractional quantum Hall effect

 

 

 

 

e,3e; e,e'2N experiments

 

 

  •  

     

  • Information Sheet

     

    Phys 540 Course Information Fall 2000

 

1. FORMAT OF COURSE:

i. Three lectures per week on Monday, Wednesday, and Friday from 10-11am in Compton 245

ii. 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%

 

Downloading Information

 

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

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