Statistical Quantum good question

[adelveis]

So here is my question. Have a 2-D electron gas where:

E = P(x)^2/(2m) + P(y)^2/(2m)

Where p^2= p(y)^2 + p(x)^2

1. How many single particle energy states are there with momentum p?

( this may be a really simple question but I need a refresher.)

2. If there are N electrons is the metal, and T=0 , find the fermi energy of the 2-D electron gas

3. Find the ave electron energy of the gas in the 2-D Fermi energy at T=0.

this last one i think I have a better idea since with the 3-D there is a factor of 1/8, the 2-D it would most likely have a factor of 1/4.

Any other help with the first 2 would be awesome!

 

[StatMechGuy]

Just start from the beginning. What's the expression of the average number of particles? From this, what's the expression for the total energy? How does that change from 3D to 2D?

You'll uncover some pretty interesting physics in 2D if you work it out, particularly with the Fermi energy.