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Homework Help: Wavepackets, expressed as eigenstates. Calculate time to tunnel to adjacent pot well?

  1. Jan 19, 2010 #1
    1. The problem statement, all variables and given/known data

    http://img29.imageshack.us/img29/5236/phst.jpg [Broken]

    2. Relevant equations

    http://img25.imageshack.us/img25/8815/11203939.jpg [Broken]

    I need to find the equation for the question.

    3. The attempt at a solution

    a)

    A bunch of waves/wave functions, that have phases/amplitudes that interfere constructively.

    b)

    |Y(x,t)|Squared = Co(/)0 + C1(/)1 Squared ???

    c)

    No idea

    d)
    i)

    A graph that slopes down, (qe) to then up to a peak, (Difference between each point is Ea) then finally back down to q.
    ii)

    Down then up then to a straight like across.






    I'd also like to know how to work out the time taken to travel to an adjacent potential well assuming Y(x,t=0) = Co(/)0 + C1(/)1
    I think (/)0 and (/)1 are the lowest eigenstates and C0 and C1 are just coefficients.

    (I think the original thread was posted in the wrong section!)
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jan 23, 2010 #2
    Re: Wavepackets, expressed as eigenstates. Calculate time to tunnel to adjacent pot w

    The complete solution was deleted (it's not allowed). So if you didn't see it:

    (a) ------------------------------

    The waves must interfer constructively only over a region.

    (b) ------------------------------

    You have forgotten some time-dependent terms.

    (c) ------------------------------

    The correct solution of (b) contains a periodic time function. It's period is the answer
     
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