Now consider a very specific initial state which is an eigenstate of So, e.g., 11)., in the following questions (as oppo

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Now Consider A Very Specific Initial State Which Is An Eigenstate Of So E G 11 In The Following Questions As Oppo 1 (8.41 KiB) Viewed 19 times

Now Consider A Very Specific Initial State Which Is An Eigenstate Of So E G 11 In The Following Questions As Oppo 2 (50.1 KiB) Viewed 19 times

Now consider a very specific initial state which is an eigenstate of So, e.g., 11)., in the following questions (as opposed to a very general initial state al 1): +6!), in the previous questions).
27. Calculate the expectation value (x( )|| $.]]x(c)) in the above state by writing Ê = - BoŜ explicitly and acting with S, on the state Ix()). 28. Since 44 = *(H, Àl) + (4) what can you infer about the time-dependence of (Sc) in the state | T), from your last response? What about (Sy) or (A) where the operator Å does not have an explicit time-dependence? 29. Consider the following statements from Pria and Mira when the electron is initially in an eigenstate of Ŝs. The Hamiltonian operator is À = - BoŜ.. • Pria: The electron will NOT be in an eigenstate of S, forever because the state will evolve in time. • Mira: I disagree. The eigenstates of $. are also the eigenstates of h. When the system is in an energy eigenstate or a stationary state, the time dependence is via an overall phase factor. The system stays in the stationary state. Since the system is in a stationary state, the expectation value of ANY operator that does not have an explicit time dependence) will not depend on time as we saw due to (x(0)||À, $.]x(t)) = 0. With whom do you agree? Explain why the other person is not correct. (a) Pria (b) Mira