Consider a system of two bound particles (e.g., two nucleons bound by the weak force), of spins S1, S2, with s1 = s2 = 1/2. In an external magnetic field, the interaction Hamiltonian is H = µB · S, with S = (S1 + S2). A random distribution (containing particles of all possible wavefunctions) of these systems is passed through a Stern-Gerlach apparatus with B = (-ax, 0, Bo+ az), with |Bo| » |az| and |Bo| » |ax|. The deflected beams are discarded. What would be the result of a measurement of S^2 on the surviving states?

(1) 0 for all of them

(2) 2 hbar^2 for all of them

(3) none of the above (explain).

Hint: what is the eigenvalue of Sz for the undeflected particles? How many distinct eigen- states of S2 and Sz correspond to it?