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Probability density doesn't oscillate with time

  1. Jan 14, 2012 #1
    why the probability density doesn't oscillate with time?
  2. jcsd
  3. Jan 14, 2012 #2

    Simon Bridge

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    It can do - and usually does, for instance, in a stationary state.
    What is the situation.
  4. Jan 14, 2012 #3


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    For a stationary state the probability density does not oscillate in time.

    The wavefunction of a stationary state does evolve in time according to ψ(x,t)=f(x)e-iEt, where f(x) is an eigenfunction of the Hamiltonian, and E is the corresponding eigenvalue. However, the probability density is the "square" of the wavefunction, ψψ*, where the multiplication of e-iEt with the complex conjugatate of eiEt gives e0=1, which doesn't change with time.

    The probability density of a general state does evolve in time, because it is the superposition of several eigenfunctions.
    Last edited: Jan 14, 2012
  5. Jan 14, 2012 #4

    Simon Bridge

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    Oh I get you - I misread.
    Yeah - the probability density of a stationary state does not vary with time, which is sort-of why it is a stationary state.
    Still need more info to answer OPs question properly.
  6. Jan 14, 2012 #5
    Here are some nice animations of probability densities varying with time:
    http://www.st-andrews.ac.uk/~qmanim/ [Broken]
    Last edited by a moderator: May 5, 2017
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