Exam

• Questions in the exam will be like those of the qualifier exams. The contents of lecture note 7 are extremely important, since they are the basic principles without which you will have a hard time doing any problem. They are analogous to these fundamental laws of classical mechanics. $$F = ma, F = \frac{dp}{dt}; \frac{d}{dt} \frac{\partial L}{\partial \dot q} = \frac{dL}{dq}; \frac{\partial H}{\partial p} = \dot q, \frac{\partial H}{\partial q} = -\dot p, \frac{\partial H}{\partial t} = \frac{dH}{dt}.$$ At the minimum, one must know the basic laws that are summarized in the table of LN 7 very well and then apply them to various problems that we did in homework and examples in lecture notes. That is, you must know when and how to start from the partition function, the Gibbs partition function, or the grand partition function, and derive every properties that you need from it. It is advised that you go over past qualifier problems (see below).

• Past qualifier exams: 2010-2012, 2005-2009, 2000-2004, 1995-1999

Homework

• Homework 5, due June 6: Phase transition (with solutions (for analytical questions))

  • Codes: Python program for calculating the fugacity of a BEC gas (first problem), Python program for Monte Carlo (last problem). – 9:55PM, May 27, 2013

  • Plotting: In case you like to plot things up in Python, here is some information that might be helpful: Plotting examples, Python, scipy, matplotlib. – 9:55PM, May 27, 2013

• Homework 4, due May 21: Quantum statistical mechanics (with solutions)

  • Correction: Problem 6 (a): the factor $\frac{1}{2}$ multiplies $\vec a \cdot \vec \sigma$ also. Also, $\sigma \rightarrow \vec \sigma$, right after "where." – 8:28PM, May 19, 2013

• Homework 3, due May 6: Ensembles, semi-classical (with solutions)

  • Addition: (Solutions) Pages 10,11: addendum (the van der Waals equation). – 10:36PM, Jun 06, 2013

  • Correction: (Solutions) $Z$ in page 9 (the power of $\bar V$, corrected). – 10:36PM, Jun 06, 2013

• Homework 2, due Apr 23: Probability (with solutions)

  • Correction: Problem 7(a): Eq. 5.22 (red). – 9:05AM, Apr 18, 2013

  • Correction: Problem 6(c): Phys. Rev. B → Phys. Rev. E. – 12:18PM, Apr 15, 2013

• Homework 1, due Apr 12: Thermodynamics – review (with solutions)

  • Correction, Addition: Problem 4 (red). Also, a sentence added at top (maximum entropy). – 8:42AM, Apr 06, 2013