Answer Happy

Note: All of the following questions refer to the system for which the Hamiltonian operator is Ĥ = -yBoŜ₂. In all of the questions below, x(t)) is the state you calculated above and assume that the coefficients a and b in the state are non-zero unless mentioned specifically otherwise.
15. Calculate the expectation value of Ŝ, in the state x(t)). Express your answer in terms of a defined earlier as a = e¹¹ cos(a) and b=e¹2 sin(a). 16. Which one of the following is the expectation value (S₂) in the state x(t))? (a) cos(20) cos(Bot+1-₂)ħ/2 (b) sin(20) cos(yBot+1-2) 1/2 (c) cos(2a) ħ/2 (d) sin(2a) ħ/2 17. Choose all of the following statements that are true about the expectation value (Sy) in the state Ix(t)): (I) (Sy) depends on time because [H, Sy] #0 (II) (S) depends on time because Ŝy has an explicit time-dependence. (III) (Sy) is time-independent because [Ĥ, S₂] = 0 (a) (I) only (b) (II) only (c) (III) only (d) (I) and (II) only