Problem 2 - 37:00

Edit: at 35:00, I said "all of the physics is contained on the left" referring to everything outside of the dimensionless integral. This was a poor choice of wording and I apologize. If the upper limit on the integral was infinity, then what I said would be true as the integral would just give a dimensionless constant. However, since the upper limit of the integral depends on the temperature, the result one obtains by doing the integral can effect the scaling of the energy with temperature!

Edit: at 36:10, I said we had a nice "closed form" expression for the energy of the Magnon gas, but we don't! We have an integral expression for the energy that we need to solve once the upper limit of integration is specified. It's still nice in the sense that instead of having to do a sum over k_x and k_y, we now have a single-variable integral to perform.

Edit: at 51:35, I said a few times that "I set mu equal to the chemical potential plus delta mu", but I meant to say that "I set mu equal to the Fermi energy plus delta mu".