4. Stationary state of infinite well (2 pts per part) A particle of mass m is in an infinite square well potential of width L, as in McIntyre's section 5.4. For all parts of this question, suppose we have an initial state vector |( 0)-E), the 3rd energy eigenstate (also called the 2nd excited state, since E is the lowest or "ground state"). You may use a computer for your integrals, but you must include the code in your solutions if you do so. Alternatively, you can do these integrals without too much pain by making use of half/double angle identities! What is the expectation value of energy at t constants of nature 0? Express your answer in terms of m, L, and A. B. Write down an expression for the time dependent state l(t)). What are the possible outcome(s) of an energy measurement at time t, and what are the corresponding probability(ies)? What is the expectation value of energy at time t? Find the position probability density as a function of time C. D. Compute

- . Use this as a sanity check on your calculations.]