Hi, I was given the following question: Show that Bose condensation does not occur in 2D. Hint: The integral you will get when you write the formula for N is doable in elementary functions. You should find that that N ∝ ln(1 − e βµ). I do indeed find that N ∝ ln(1/(1 − e βµ)) ∝ ln(1 − e βµ), but I not sure how this tells me that Bose condensation isn't occurring. I have a feeling that Bose condensation is not occurring because the equation n/n_Q = f(βµ) always has a solution (n/n_Q ∝ ln(1/(1 − e βµ)), and ln(1/(1 − e βµ)) takes any value from 0+ (i.e. infinitesimally above zero) to +infinity if you have a look at it), where n_Q is the quantum concentration, some constant, and n = N/A, where A is the area of the 2D system, N is the total number of particles in it. By contrast, when in 3D, you find that there isn't always a solution and there is some critical temperature where a transition takes place; the f(βµ) in that case looks a little like ln(1/(1 − e βµ)) except for the fact that it hits the vertical axis at a value of about 2.6 ish before cutting off for βµ > 0. Is this correct? Further to this, how can N vary with temperature, i.e. where are the particles going to/coming from when the temperature changes? Is this just some weird unphysical result? Sorry if this is in the wrong forum - I know it's sort of quantum mechanics but it's part of a statistical mechanics course.