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If a wavefunction can only collapse onto a few eigenstates

  1. Mar 11, 2009 #1
    I just started learning QM. I was wondering, if a wavefunction can only collapse onto a few eigenstates, how come the probability distribution graph is a usually continuous one? :S
     
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  3. Mar 11, 2009 #2

    chroot

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    Re: Eigenstates

    Imagine a probability space spanned by two eigenstates -- it's a 2D space, containing an infinite number of points. At each point in the space, there's a specific probability of collapsing onto each eigenstate. That's a continuous quantity.

    - Warren
     
  4. Mar 11, 2009 #3
    Re: Eigenstates

    I don't quite get it :S. From my understanding, the probability distribution graph depicts the probability of where the particle will collapse. But you're saying that it actually represents the probability of a particle, currently at a particular position on the graph, collapsing onto an eigenstate?
     
  5. Mar 11, 2009 #4

    chroot

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  6. Mar 12, 2009 #5
    Re: Eigenstates

    I was referring to a graph of the square of the wavefunction vs position. That's what the textbook that I'm reading (Griffiths) uses to depict the probability of where a particle associated with some wavefunction will collapse.. It's only taking 1-D into account I think.
     
  7. Mar 12, 2009 #6

    chroot

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    Re: Eigenstates

    I have Griffiths... which page number? I'll pull it out.

    - Warren
     
  8. Mar 12, 2009 #7
    Re: Eigenstates

    Just something like on page 3, fig 1.2 where it's a continuous graph..
     
  9. Mar 12, 2009 #8

    chroot

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    Re: Eigenstates

    The wavefunction is a function of all space. If you give me any point in space, I can give you the value of the wavefunction there. Therefore, the wavefunction is continuous. The book hasn't even introduced eigenstates yet.

    - Warren
     
  10. Mar 12, 2009 #9

    alxm

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    Re: Eigenstates

    The states are discrete, but the corresponding eigenfunctions aren't discrete in space. Consider the particle-in-the-1D-box example. Every wave function is continuous with a value at every point from 0 to L.

    So obviously a state that's a superposition, a sum, of several eigenfunctions is also going to continuous and defined from 0 to L, and so is the absolute square of that superposition.
     
  11. Mar 12, 2009 #10

    dx

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    Re: Eigenstates

    Eingenstates of what? A particle in a box has a discrete energy basis, but the position basis is continuous. The diagrams of wavefunctions are usually drawn in position space, so they will be continuous.
     
    Last edited: Mar 12, 2009
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