Working in the N;SPMgt;;SPMgt;1 limit, compute the total energy E for N electrons which have been allowed to settle into their lowest energy configuration in an infinite square well potential of size L.
Give the analogue of the idea gas law P=(N/V)KT for this case,
namely compute the average force F on the walls of the
box in terms of the density 
of particles in the box.
Hints: Recall that only two electrons may settle into each state. Also, you may wish to use the sum
