An c-polarised beam of atoms with angular momentum l = 1 and m = 0 passes between the poles of two stern-gerlach magnets in sequence. the first is oriented in the z direction and the second in the x direction; all beams separated in the first magnet pass between the poles of the second. (a) how many beams emerge from the second magnet? explain. (b) what are the polarisations (angular momentum states) of those beams and what fraction of atoms emerge in each? (c) the first stern-gerlach magnet is replaced by a region of uniform magnetic field oriented in the z direction. the hamiltonian of an atom in this field is î = -~bî, where b is the magnetic field magnitude and y is a constant. as a general rule, how many beams emerge from the second stern-gerlach magnet, and in what polarisation states? explain. (d) show that there exists a special (nonzero) choice of b for which only one beam emerges from the arrangement in part (c).