Consider a system of four noninteracting identical spin 1/2 particles (each of mass m) 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 and the first three excited states. Draw a figure showing how the particles are distributed among the levels.