The dependence between density and the Fermi energy to 2Dfree electronic gas
Answers
Answered by
2
Answer:
I am assuming that you are referring to the free electron model in 2d.
Consider N electrons confined to a rectangular box with sides lx,ly .The Schrodinger equation for a free 2d system is
−ℏ22m(∂2∂x2+∂2∂y2)ψ=Eψ
The solutions are
ψ(x,y)=2lxly−−−√sin(nxπlxx)sin(nyπlyy)
The allowed energy levels are
E=ℏ22m(n2xπ2l2x+n2yπ2l2y)
Let
k⃗ =(nxπlx,nyπly)
Then
k2=n2xπ2l2x+n2yπ2l2y
So
E=ℏ2k22m
Similar questions
Geography,
3 hours ago
Math,
3 hours ago
Math,
6 hours ago
Psychology,
8 months ago
English,
8 months ago