Physics 971: Statistical Mechanics

Syllabus


Office hours:
Monday 10-11am
Wednesday 10-11am
or by appointment
Office: 330 Cardwell


The final has been graded and can be picked up in my office.
The average score was 80% (about the same as the midterms).
The standard deviation was about 13 points (much narrower distribution than midterms).

Here is the final. solutions

The final is a 24-hour take home exam. It will be posted on this website at 10am on 12/12. It is due in my office 12/13/12 at 10am. You may use any class materials (lecture notes, textbook, homeworks, posted solutions) but no outside materials (other books, internet). Use of Mathematica is acceptable, but please indicate where it has been used. Work alone, and do not discuss the exam with your classmates until all exams have been turned in. You may email me for questions or clarifications, and all responses will be posted here to be shared with the class.

Questions and Clarifications:

• Question 1b: The particle is free to explore the entire lattice (assumed to be infinite) not just the states you looked at in part (a).
• Question 2b: The factor of two in the interaction term is to fix the double counting of bonds.
• Error: There is an mistake in question 3. The prefactor in the correlation of the random forces should be 6 (not 2 as originally written). The extra factor of three arises because we get 2kT/B in each of the three dimensions.
• A revised copy of the final has been uploaded. I apologize for the error.
• Question 3 is in three dimensions (x, x-dot, and f are all bold vectors). Hint: each of the dimensions is independent of the others.
• Question 4: The electrons in the metal have both a potential energy and a kinetic energy. The electrons in the semiconductor only have an energy epsilon (which accounts for both potential and kinetic energy).
• Question 1a: Q: Do i have to find more than one entropy? A: Yes, you need to compute 5 different entropies.
• Question 1a: Compute the entropy for 5 different values of E.
• Question 4: Q: Can you explain 'Ns degenerate orbitals of energy E'? Does it mean that all the electrons in semiconductors have the same energy?
  A: The short answer is: yes, assume that all electrons in the semiconductor have the same energy.
  The long answer:
  Usually what happens in a semiconductor is that each atom has only one electron orbital that needs to be considered (all the other orbitals are far below the Fermi level so that they are always occupied). These are the orbitals that I am assigning an energy 'epsilon'--there is one orbital associated with each atom in the solid, and all the atoms are identical, so all the orbitals have the same energy.
  Now, in real materials there will be weak interactions between these orbitals that breaks the degeneracy. This results in the band structure of the solid (Bloch waves). But I am asking you to ignore this complication (it will not change the answer).
• Question 4: e*Phi is not the only contribution to the chemical potential of the metal electrons.

This is a copy of the 2011 final. solutions
This is a copy of the 2011 midterm.

Midterm #1 solutions.
Midterm #2 solutions.

Homework assignments:

Homework 1 Due 9/4/12 solutions

Homework 2 Due 9/18/12 solutions

Homework 3 Due 10/9/12 solutions

Homework 4 Due 10/18/12 solutions

Homework 5 Due 10/25/12 solutions

Homework 6 Due 11/16/12 solutions

Homework 7 Due Friday 12/7/12 solutions






Schmit Group Home | Physics Department | Kansas State University