12. Consider the following conversation between Pria and Mira about (S.) in state x(t)): • Pria: Since the state of the

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12 Consider The Following Conversation Between Pria And Mira About S In State X T Pria Since The State Of The 1 (55.81 KiB) Viewed 39 times

12. Consider the following conversation between Pria and Mira about (S.) in state x(t)): • Pria: Since the state of the system x(t)) evolves in time, the expectation value (S) will depend on time. • Mira: I disagree with the second part of your statement. The time development of the expectation value of any operator Å is given by ) = ([H, Â])+(ª). In our case, [A, S₂] = 0 and the operator Ŝ, does not have any explicit time dependence so = 0. Thus, 0 and the expectation value will not change with time. = With whom do you agree? (a) Pria (b) Mira (c) Neither 241 13. Which one of the following is the expectation value (S₂) = (x(t)|sz|x(t))? (a) cos(20) cos(yBot) h/2 (b) sin(2a) sin(Bot) ħ/2 (c) cos(2a) ħ/2 (d) sin(2a) ħ/2 14. Which one of the following is true about the expectation value (S₂) in the state x(t))? (a) (S₂) depends on time because [Ĥ, Ŝ₂] #0 (b) (S) depends on time because Ŝ, has an explicit time-dependence. (c) (S₂) is time-independent because [Ĥ, Ŝ₁] = 0 (d) None of the above.