Consider a system of three 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 energy and wave function of the ground state and the first and second excited states when the three particles are (a) spinless and distinguishable with m1<m2<m3; (b) identical bosons; (c) identical spin 21 particles; and (d) distinguishable spin 21 particles.