Answer Happy

4. (25) Let S ms) denote a spin eigenstate of total spin S and spin 2-component ms. Consider two non-interacting spin / particles and for each particle denote the spin up state 1 %) as f and the spin down state 142-) as 1. (a) (2) What are the possible values of the total spin angular momentum of the combined two-particle system? Express each of the spin angular momentum eigenstates of the combined system S ms) in terms of 1 and 1. (b) (3) Define the total spin operator for the two particle system as S = SS where $(1) is the spin operator of particle 1 given by S(1) = S(+503 +5,"R, and (2) is the (1) spin operator of particle 2 given by $(2) = 5.2i+si+sR. Show that S = ($)+$2)-(S) + S 2)) = ($!)2 + (52))2 +2 1.512) (c) (10) Using the spin operators (1) s(1) s.) and (2) s(2) show that: 5.52)(14) (2 - 11). 2 17 (d) (10) Use the results above to show that S4 10) = 2 | 10) and S400) = 0. = 5