(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider a gas of non interacting electrons in two dimensions with electronic density n by unit of area and mass m. The gas forms a square of sides L.

1)Assume periodic boundary conditions, find the density of states by unit of area.

2)Find the Fermi energy in function of m and n.

3)Calculate the increase of energy that N particles produce (assuming [itex]k_BT << E_F[/itex] where [itex]E_F[/itex] is fermi's energy) and then calculate the specific heat for T~0K.

2. Relevant equations

Problably a lot, I have no reference textbook so all on the internet I guess.

3. The attempt at a solution

Totally stuck on part 1).

Let me see if I understand the question correctly, they are asking me the "density of state" function divided by a unit of area? In other words, [itex]\frac{g(E)}{1au}[/itex]?

I'm reading stuff at hyperphysics (http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/eedens.html#c1), apparently [itex]n=\frac{g(E)}{e^{(E-E_F)}/(k_BT)+1}[/itex]. But I must determine E in function of L I guess.

For a 2d quantum well, the allowed energies are [itex]E_m=\frac{m^2h^2}{8mL^2}[/itex] if I'm not mistaken. What bothers me here is the natural number m and the fact that I expressed a formula involving [itex]E_F[/itex], something I'm asked to find in the next question, so that I'm guessing I'm not going in the right way.

I'd love some help, I'm really struggling with this course (I have no textbook).

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# Homework Help: Fermions, density of states

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