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Week 9

modified 9Mar2018 at 3:10PM by Paul Crowell 

I am assuming that you will read the section on magnetotransport and the Hall effect (pp. 152  155), which I did not get to in lecture. We will start with Chapter 7 on March 20. This chapter is in a sense the crux of the class. What happens to electronic states (originally planes waves in an empty box) when we "turn on" the periodic potential? Although this is a difficult problem to solve analytically (except in some special cases), there turn out to be some global rules (such as Bloch's theorem) that allow us to make sense of what is going on. My goal is for you to understand why gaps form, the relation to symmetry, and how this impacts the behavior of real materials. Problem Set 6 is now posted and will be due on March 27th. 
Lecture Slides

modified 8Mar2018 at 7:28PM by Paul Crowell 

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Problem Sets

modified 10Mar2018 at 1:40PM by Paul Crowell  


Week 8

modified 1Mar2018 at 9:31PM by Paul Crowell 

We will continue with Chapter 6. In all likelihood I will not start Chapter 7 until after spring break, but read pp. 163  167 by Thursday, March 8. The solutions to Quiz 1 are now posted. Professor Valls will lecture on Tuesday. The topics will be thermodynamics of the electron gas (e.g. specific heat) and transport in the relaxation time approximation. I will return on Thursday (I hope) and do magnetotransport (a first pass), thermal transport, and perhaps an aside on optical properties of metals. Problem Set 5 is due Thursday, March 8. 
Quiz 1 is posted here.

modified 9Mar2018 at 6:48PM by Paul Crowell 

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Week 7

modified 25Feb2018 at 8:17PM by Paul Crowell 

Tuesday's lecture will cover some more topics in quantum mechanics, some of which appear in Kittel's Chapter 6, including spin, FermiDirac statistics and the FermiDirac distribution. I will then continue with a discussion of Dirac notation and matrix mechanics. Thursday's lecture will cover most of the remainder of Chapter 6, through approx. p. 152. Problem Set 5 is posted. It will be due Thursday, March 8. My office hour this week will start at 3:15, and I will shift it from 3:15  5:00. 
Week 6

modified 17Feb2018 at 12:37PM by Paul Crowell 

Problem Set 4 is posted and will be due Friday, February 23rd, by 5 PM. You may either put the problem set under my office door (PAN 220) or upload a SINGLE PDF file to the class Moodle Page: https://ay17.moodle.umn.edu/course/view.php?id=10110 The lecture on Tuesday, February 20 will cover material in the second part of Chapter 5, including the generalization of the phonon density of states, van Hove singularities, anharmonicity, and thermal transport. We will start Chapter 6 (electrons) the week of February 27. There will not be a lecture on Thursday, February 22nd. I cannot overemphasize the importance of the density of states, and how we start with a density of states in kspace, which is always (L/2\pi)^d, (where d is the dimensionality) and, with knowledge of the dispersion relation E vs. k, calculate the density of states with respect to energy (or frequency). Depending on the type of particles we are dealing with (phonons, electrons, etc.) the dispersion relation and hence the form of the density of states with respect to energy will vary. In contrast, the details of the Debye calculation are not important. If you have not had statistical mechanics, do not worry about it. You should know that the acoustic phonon contribution to the heat capacity scales as (T/\Theta_D)^d (where d is the dimensionality). We will discuss the contribution from optical phonons on Tuesday. 
Quiz 1

modified 14Feb2018 at 11:43AM by Paul Crowell  

The first quiz will be available (by download from the web site) next Thursday. It will be similar in format to the quiz from last year, which is posted here. This year's quiz will only cover material up through Chapter 5 (phonons). I will probably give you 2 hours, but I am inclined to make it closed book (so that I can ask easier questions!). You can take it when you wish and hand it in on Tuesday, February 27. There will not be a lecture on Thursday, February 22nd.

Week 5

modified 14Feb2018 at 10:06AM by Paul Crowell 

Problem Set 4 is posted and will be due Friday, February 23rd, by 5 PM. You may either put the problem set under my office door (PAN 220) or upload a SINGLE PDF file to the class Moodle Page: https://ay17.moodle.umn.edu/course/view.php?id=10110 Reading: Kittel Chapters 4 and 5. Analogous chapters in Ashcroft and Mermin are Chapters 22  24. Tuesday's lecture: Phonon dispersion relations, optical and acoustic modes, phonons and momentum Thursday's lecture: Phonons: thermal properties Problem Set 3 is due Thursday 
Week 4

modified 8Feb2018 at 2:34PM by Paul Crowell 

Reading: Kittel, Chapter 4. This material is covered (much more thoroughly) in Ashcroft and Mermin, Chapter 22. A&M have four chapters on phonons. Neutron scattering gets its own chapter (24) as do anharmonic effects (25). Tuesday's Lecture: We will spend the first few minutes discussing a couple points from the problem set. After that, I will turn to topics in quantum mechanics (the PHYS 5012 students can leave at that point). Thursday's Lecture: I will conclude the brief review of chemical bonding and then start on phonons. Problem Set 3 will be posted shortly. It will be due Thursday, February 15th. 
Week 3

modified 2Feb2018 at 12:21AM by Paul Crowell  

Problem Set 2 is posted. It will be due Tuesday, February 6th. Because on Thursday I mutilated the discussion of the Miller indices (hkl) in terms of the shortest reciprocal lattice vector perpendicular to a set of lattice planes, I am attaching a discussion here. Both lectures this week will be on "core material" (i.e., no special quantum mechanics lecture). I will probably start the material in Chapter 3 of Kittel (crystal binding) in the second half of Thursday's lecture. I will have relatively little to say about this beyond what is in the text. For those looking for more, I recommend Chapters 19 and 20 of Ashcroft and Mermin.

Office Hours

modified 18Jan2018 at 7:19PM by Paul Crowell 

My office hours will be Wednesday 2:45  4:30 and by appointment. 
Week 2

posted 18Jan2018 at 7:11PM by Paul Crowell 

The lecture on Tuesday, January 23 will continue the "primer on quantum mechanics" from last Tuesday. I will cover Hilbert space, Dirac notation, operators, expectation values, and the matrix formulation of quantum mechanics. I will probably not get to spin. The lecture on Thursday, January 25th will continue our discussion of crystal structure, with the concept of reciprocal space and the basics of diffraction. Problem Set 1 will be due on Thursday, January 25th. Note that the last problem (on diffraction) does not have to be handed in this Thursday. It is on there to give you a head start on next week. 
Week 1

posted 16Jan2018 at 6:01PM by Paul Crowell 

Reading: Kittel, Chapters 1 and 2 We will spend the first two weeks on "structure and symmetry," with an emphasis on the important crystalline systems and the notion of reciprocal space. I am not going to emphasize the mathematical aspects of symmetry, such as point groups and space groups. If you are interested, Ashcroft and Mermin address these (slightly) in their Chapter 7. The first problem set is posted. Because we are interleaving the first couple lectures on quantum mechanics, I may adjust the due date, but for the moment assume it is due Thursday, January 25. 