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Wavefunction with changing potential

  1. Oct 18, 2012 #1
    1. The problem statement, all variables and given/known data
    See the attachment for question and solution


    2. Relevant equations
    See the hint in the question


    3. The attempt at a solution
    In part (c), it asks about the probability of finding the particle in ground state.

    As far as I know, we need to write the wave function in terms of eigenfunction first.
    i.e. ψ(x,t)=[itex]\sum c_{n} f_{n} (x) e^{-iωt}[/itex]
    Ground state correspond to n=0. Therefore, the probability we want is [itex]c_{0}[/itex]

    Also [itex]c_{0}[/itex]=[itex]\int ψ^{*} f_{0}[/itex]

    [itex]f_{0}[/itex] is provided in the hint which is [itex]\sqrt{\frac{\alpha}{\sqrt{\pi}}}e^{\frac{-\alpha^{2} x^{2}}{2}}[/itex]
    But I have no idea what [itex]ψ^{*}[/itex] is.

    Also I have no idea what is going on in the solution
     

    Attached Files:

  2. jcsd
  3. Oct 18, 2012 #2
    Also, I don't understand the solution for part d, can anyone explain it to me?
    Especially why n must be even?
     
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