Consider a rectangular box of sidesLx,Ly,Lzwith hard wall boundary conditions (Unlike periodic boundary conditions used in class). a) Find the energies of the eigenstates in this box. IfNspin-1/2 electrons are put into this box (AssumeN>>1) and, b) Find the energy required to add one more electron. c) Total energy of the system. Your results should be equivalent to what was found with periodic boundary conditions in the thermodynamic limit.