So forNparticles filling the levels,(n^2 x+n^2 y+n^2 z)(^32)
max=
6 N
π.
(n^2 x+n^2 y+n^2 z)max=(
6 N
π)^23
The energy corresponding to this is the Fermi energy.EF=
π^2 ̄h^2
2 mL^2(
6 N
π)^23
2.*We putNfermions of massminto a (cold)one dimensional boxof lengthL. The particles
go into the lowest energy states possible. If the Fermi energy is defined as the energy of the
highest energy particle, what is the Fermi energy of this system? You may assume that there
are 2 spin states for these fermions.