Course Syllabus


An introduction to phenomena that illustrate basic principles of solid state physics using undergraduate quantum mechanics:

Phys 731 elucidates a set collective quantum phenomena that occur in solid state systems by taking advantage of quantum mechanics at the advanced undergraduate (Griffiths) level (this is what takes this course beyond the undergraduate one) . 







Some of the topics covered are (suggestions welcome):

  • Second quantization for the many-electron gas
  • Hartree-Fock for electrons
  • Screened Coulomb interactions (dielectric function)
  • Fermi surface and Fermi liquids - zero sound
  • Collective excitation of the electron gas (plasmons and magnons)
  • Second quantization for Bosons
  • Bogoliubov description of sound in superfluids
  • Phonons and magnons  in solids as examples of Bosons
  • Bloch's theorem - topological insulators
  • Electromagnetic response - Quantum oscillations, Bloch oscillations
  • Electron-phonon interaction
  •  Phonon mediated electron attraction
  • BCS theory of superconductivity
  • Ginzburg-Landau theory





Required Resources

Course website:

Text book: A Quantum approach to Condensed Matter Physics, Taylor and Heinonen, 1st edition, Cambridge University Press 2002.








Dr. Jay D. Sau

Class Meets

Tuesdays & Thursdays

11:00 am – 12:15 pm

PHY/Toll #1204

Office Hours

PHY/Toll #2330

by appointment





Suggested Prerequisites

Undergraduate quantum mechanics (PHYS 401/402 or equivalent)

Undergraduate statistical mechanics (Phys 404 or equivalent)

Course Communication

All updates and information regarding the course will be made using the announcements on ELMS – please make sure your ELMS settings do not delay announcements. I may or may not repeat in class.

Please send any questions or notifications of absences that you need to inform me preferably by email (see above).  



Campus Policies

It is our shared responsibility to know and abide by the University of Maryland’s policies that relate to all courses, which include topics like:

  • Academic integrity
  • Student and instructor conduct
  • Accessibility and accommodations
  • Attendance and excused absences
  • Grades and appeals
  • Copyright and intellectual property

Please visit for the Office of Undergraduate Studies’ full list of campus-wide policies and follow up with me if you have questions.


Activities, Learning Assessments, & Expectations for Students

Lectures: Class time will be occupied by lectures that follow a set of notes that closely follow sections in the textbook. In a few cases I will follow a different textbook, which I will point out. I will post my notes online in this case. In addition to explaining the physical intuition behind concepts I will provide mathematical derivation of some of the more important results where the derivation is instructive. A firm grasp of quantum mechanics at approximately the advanced undergraduate level will be needed to follow parts of the lectures as well do some of the homeworks. The thorough use of quantum mechanics is what distinguishes the graduate solid state course from the undergraduate one.

Participation: The lectures assume that you are keeping track of the material of the previous lecture. This will enhance your learning and participation in the class, which is crucial to the classes success. To ensure a minimal level of participation, I will keep track of your participation through questions you ask or answer. You get full credit for participation if you ask or answer 6 questions in the semester related to the material presented in the lectures. Participation points of 2/lecture will be added to your grades within 24 hours of the lecture you participated in (i.e. asked/answered a relevant question/clarification).  I might forget to credit you for this. IT IS YOUR RESPONSIBILITY TO EMAIL ME IF I FORGET TO ADD THIS WITHIN TWO DAYS.  Late (by more than a few days) may or may not be credited depending on whether I remember.

Homework : Problem sets will be posted as assignments on ELMS. The problems can also be downloaded from the assignments folder. Homework submission should be preferably by paper in class or at instructor office. Email submission to TA is allowed but should not be hand written. In case of email submissions, please also hand in a paper submission at a later date to facilitate return at graded homeworks. Homework will be assigned roughly once a week, and is to be turned in at the beginning of class on the due date. Homework will typically be posted on Friday and due the Thursday two weeks later (i.e. about 11 days). 20% will be marked off on homework turned in after the end of class. Homeworks turned in after the solutions are posted will not be graded. If you cannot attend class, please get your homework to me before class starts.  New assignments will be posted on the course website, along with the homework solutions.  Homework problems are carefully chosen to highlight some of the important topics covered in lecture, complete some of the important steps, as well as important applications of the ideas. It is important that you carefully complete and make sure you understand all of the homework. You are encouraged to work with others on homework, however, it is forbidden to blindly copy another person’s work. There are 9 homework sets and one will be dropped. 



Grades are not given, but earned.  Your grade is determined by your performance on exams, homeworks and participation in the course and is assigned based on your score according to a curve. Typically I follow a curve scheme where the median score would be graded at B+. The lowest grade would be B- (very few). The top grades will be A+ and As. The number in each category would be roughly equal depends on appropriate breaks in the score distribution. 

Of course, all this being said this rule is subject to change depending on the performance of the class. If some students do extremely poorly (e.g. score well below 40%) I might consider going below B- for the lowest grade.  On the other hand, if everyone does well (i.e. above 90%) I have no hesitation giving the entire class an A. Also, if someone scores above 80 that is a B or better independent of whether the average is above 80.

If earning a particular grade is important to you, please speak with me at the beginning of the semester so that I can offer some helpful suggestions for achieving your goal.

All assessment scores will be posted on the course ELMS page.  If you would like to review any of your grades (including the exams), or have questions about how something was scored, please email me to schedule a time for us to meet in my office.

Late work (as explained in the instruction) will not be accepted for course credit so please plan to have it submitted well before the scheduled deadline.  I am happy to discuss any of your grades with you, and if I have made a mistake I will immediately correct it.  Any formal grade disputes must be submitted in writing and within one week of receiving the grade. 

Learning Assessments


Category Weight

Participation points



Homework (out of 9 assignments)




Course Schedule


Week 1

Tuesday, January 29

  • Semiclassical phonons (1.2)

Thursday, January 31

  • Semiclassical solitons, plasmons (1.3, 1.5)

Week 2

Tuesday, February 5

  • Plasmons (1.5)

Thursday, February 7

  • Magnons (1.4)

Week 3

Tuesday, February 12

  • Semiclassical interacting fermi gases (1.6) 

Thursday, February 14

  • Collective modes of Fermi liquids (1.6, Landau-Lifshitz v9)

Week 4

Tuesday, February 19

  • Collective modes - role of dimensions (Mermin-Wagner)

Thursday, February 21

  • Measurement of collective modes (role of conservation - & symmetry)

Week 5

Tuesday, February 26

  • Second quantization for electrons (2.1-2.3)

Thursday, February 28

  • Anti-ferromagnetism - Heisenberg superexchange.

Week 6

Tuesday, March 5

  • Hartree-Fock for electron gas (2.4)

Thursday, March 7

  • Hartree-Fock for electron gas  contd (2.4)

Week 7

Tuesday, March 12

  • Ferromagnetism & Wigner crystal

Thursday, March 14

  • Perturbation theory for electrons ( 2.5 )
  • Density operator, screening, spin-waves ( 2.6-2.8 )

Week 8

Tuesday, March 26

  • Plasmons and Thomas Fermi from Lindhard dielectric

Thursday, March 28

  • Bloch's theorem: (Chapter 4)

Week 9

Tuesday, April 2

  • example hexagonal lattice/graphene (Chapter 4)

Thursday, April 4

  • Band-gap, effective mass and Dirac points in Graphene
  • Symmetry in band structure (Chapter 4)

Week 10

Tuesday, April 9

  • Bernevig-Hughes-Zhang model for topological insulators  ( Chapter 4 )

Thursday, April 11

  • Electric fields - transport, Block oscillations, Landau-Zener breakdown (Chapter 4)

Week 11

Tuesday, April 16

  • Magnetic fields and quantum oscillations, Lifshitz-Kosevich formula (Chapter 4)

Thursday, April 18

  • Quantum Harmonic oscillators, quantization for Bosons (3.1 - 3.3 )
  • Bogoliubov excitations in superfluids (3.4)

Week 12

Tuesday, April 23


  • Electron phonon interaction ( Chapter 6 )

Thursday, April 25

  • Quantization of phonons ( 3.5-3.8 )
  • Kohn-anomaly (Chapter 6)
  • Peierls instabilities (chapter 6)
  • Phonon-induced electron pairing ( Chapter 6 )

Week 13

Tuesday, April 30


  • Phenomenology of superconductivity: transport and gap ( Chapter 7 )

Thursday,  May 2

  • Phenomenology of superconductivity: coherence ( Chapter 7 )

Week 14

Tuesday, May 7

  • Cooper pairing and the BCS Hamiltonian ( Chapter 7 )

Thursday, May 9


  • BCS ground state wavefunction and quasiparticle gap ( Chapter 7 )

Week 15

Tuesday, May 14

  • BCS gap equation and transition temperature ( Chapter 7 )
  • Josephson effect and Landau-Ginzburg theory ( Chapter 7 )

Thursday, May 15



Note: This is a tentative schedule, and subject to change as necessary – monitor the course ELMS page for current deadlines.  In the unlikely event of a prolonged university closing, or an extended absence from the university, adjustments to the course schedule, deadlines, and assignments will be made based on the duration of the closing and the specific dates missed.

Course Summary:

Date Details Due