For a particle of mass m in a three-dimensional cubic box with potential energy 0, 0s r, y, z a v(z, y, z) = oo, otherwise the normalized wave function within the bor and the energy are given respectively by (with ni, n2, n3 = 1, 2, 3, ) 3/2 n2ty al sinsin sill( if the particle is in the state nin2n3) consider now two noninteracting identical particles of mass m and spin 1/2 are placed in this cubic box. (a) if measurement of their energies yields 3π2h2/ma2, what is the total wave func- tion of these two particles? and, what are the possible values of the total spins of these two particles? (b) if measurement of their energies yields 6π2e/ma2, what is the total wave func- tion of these two particles? and, what are the possible values of the total spins of these two particles? note that the total spin parts of the two particles χ8.ms are given by /2 xi,0 = v2