1. 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 |(t = 0)) = E₂), the 2nd energy eigenstate. (This is also called "the 1st excited state", since E₁ is the lowest state or "ground state".) c) Compute (p(t)). Does your answer make physical sense? Why? d) Calculate the probability that a measurement of position will find it somewhere between L/4 and 3L/4. e) Compute Ax and Ap for the above state, and comment on their product AxAp. Feel free to use a computer for any integrals you find nasty. Recall from earlier this term how we define the standard deviation: Ax = [y]x²|y) — [y]x]y}²
1. 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 |(t = 0)) = E₂), the 2nd energy eigenstate. (This is also called "the 1st excited state", since E₁ is the lowest state or "ground state".) c) Compute (p(t)). Does your answer make physical sense? Why? d) Calculate the probability that a measurement of position will find it somewhere between L/4 and 3L/4. e) Compute Ax and Ap for the above state, and comment on their product AxAp. Feel free to use a computer for any integrals you find nasty. Recall from earlier this term how we define the standard deviation: Ax = [y]x²|y) — [y]x]y}²
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