Consider a system of five noninteracting electrons (in the approximation where the Coulomb interaction between the electrons is neglected) that are confined to move in a common one-dimensional infinite potential well of length L=0.5 nm: V(x)=0 for 0<x<L and V(x)=∞ for other values of x.
(a) Find the ground state energy of the system.
(b) Find the energy of the first state of the system.
(c) Find the excitation energy of the first excited state.