**Important Things to Note:**

There’s a lot of stuff here; bosons, fermions and photons; einstein condensation, high temperature limits, black body radiation. While this topic is very content dense, the nice thing about this topic is that it’s very difficult to construct tricky questions once you understand it. If you master this topic you are almost guaranteed to get a lot of points on the comprehensive exam. Additionally, once you understand the math, you’ll see that the calculations for bosons, fermions and photons are almost identical.

Spend most of your time trying to understand the grand canonical ensemble and the math used in quantum gases. After you’ve mastered that, then worry about the particularly properties and details of quantum gases.

## Understand EVERY WORD of these:

SUPER important prerequisite math from Professor Mona Berciu at University of British Columbia

(Read and reread until you can derive everything she does from scratch. Mastering and understanding exactly how to calculate the density of states of a quantum gas will make the rest of quantum gases MUCH more clear.)

(If you completely understand these lecture notes, you should be able to handle almost any problem given on the comprehensive exam!)

Connected to these topics is some additional math that finds approximations for some messy integrals we will encounter. It’s not a bad idea to skim this, but it’s a little bit too involved to really be worth your time. My advice is to just trust the answer to the summerfelt expansion and not to worry about going through its derivation.

**Most important Problems & Solutions:**

- Derive the density of states for a bosons, fermions, and photons for 1D, 2D, 3D (so 9 cases). Do everything from first principles with NO references!
- Problem #1 (solution)
- Problem #3 (solution)
- Problem #2 in SBU Fall 2015 Comps (the given solution is terrible; later I’ll link my solution at some point)
- Problem #2 (solution)
- Can a 2D bose gas create Bose-Einstein condensation?
- Problem #1 in SBU Spring 2016 Comps
- Problem #1 in SBU Spring 2015 Comps