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Quantum mechanics - Help

  1. Mar 25, 2005 #1
    Please, can someone help me with this problem:

    A particle is in the ground state of 1D infinite square well with walls at x=0 and x=L. At time t=0 the walls are suddenly removed so that the particle become free.
    A) Find the probbability W(p)dp=|f(p)|^2dp that a measurement of the momemntum of the particle will produce a result between p and p+dp
    B) Calculate the corresponding probabbility W(p)dp=|f(p)|^2dp for the case in which the particle is initially in the n-th energy eigenstate. Show that your result is in agreement with uncertaity principle and that for large n it is in accord with the correspodence principle

    Thank you in advance
  2. jcsd
  3. Mar 25, 2005 #2


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    1.What's the initial waveunction in the coordinate representation (HINT:It's the one which is obtained solving the SE for this model)?
    2.TransFourier i,take the square modulus and obtain the probability density W(p)_{0}.
    3.Use the fact that the free particle hamiltonian determines a unitary evolution and that the evolution operator has a simple form (complex exponential).
    4.What does it (v.#3) mean for the evolution of probability density in time...?
    5.For point "a",u'll need to make the "n=1" in the general solution (v.#1).

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