Consider a system of four noninteracting particles that are confined to move in a one-dimensional infinite potential well of length a: V(x)=0 for 0<x<a and V(x)=∞ for other values of x. Determine the energies and wave functions of the ground state, the first excited state, and the second excited state when the four particles are
(a) distinguishable bosons such that their respective masses satisfy this relation: m1<m2<m3<m4, and
(b) identical bosons (each of mass m).