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Does the wavefunction have a zero value anywhere?

  1. Nov 2, 2009 #1
    Does the wavefunction have a zero value anywhere??

    Are there any places in the universe where a wavefunction has a 0 value? Or does the wavefunction have a non-zero value for everywhere in space? (0 doesn't equal incredibly unlikely).
    ---
    Also, let's assume the theory on the planck length is correct (perhaps it's been proven, I dunno I aint a physicist!), what happens if two particles collapse at the exact same moment -the same planck time slice - into the exact same place in space. Would there be some massive release of energy? Is there something inbuilt that stops this from ever occuring? Do we not know the answer to this at this point in time?

    I assume this can't happen as this would have inevitably happened in the electron cloud and we would have observed it by now.. right?
     
  2. jcsd
  3. Nov 2, 2009 #2
    Re: Does the wavefunction have a zero value anywhere??

    A plane wave is a useful approximation of a wave packet which is localized in a large but finite volume V (the size of your experimental setup). Outside it the wave function is zero.

    Plank length is a very short distance. All elementary particles are much "larger". This distance appeared from playing with physical constants rather than from some phenomenon description. It has no particular meaning in physics.
     
  4. Nov 2, 2009 #3
    Re: Does the wavefunction have a zero value anywhere??

    Yes, there are many!
    Interference or superposition is one of the main features of Quantum Mechanics. As an example, electron beam passing two slits makes the interference pattern on the screen. We can say with 100% probability that electorons cannot come this and this points on the screen. Wave function are zero on these points.
     
    Last edited: Nov 2, 2009
  5. Nov 2, 2009 #4
    Re: Does the wavefunction have a zero value anywhere??

    I was under the assumption from Brain Greene's book that the wavefunction always has a non-zero value and what we see in everyday life is just the most likely (by an extreme, unimaginable amount) occurance occuring.

    He gave the example that it is actually possible for every particle in every oxygen atom in any given room to collapse onto the dark side of the moon leaving you dead, except it is so unlikely that it'll most likely never occur.

    Perhaps the dark spots on the screen in the double slit experiment are areas of the wavefunction that are incredibly close to 0 and we're unlikely to see any experimental evidence of a statistical blip occuring whereby the electron actually collapses into the dark spot within our lifetimes?

    Or then again what you said could be right and my conclusions could be wrong.
     
  6. Nov 2, 2009 #5
    Re: Does the wavefunction have a zero value anywhere??

    Of course. We know that the many-electron wave function for a bunch of fermionic particles has to be antisymmetric (it changes sign under exchange of two particle labels). This implies that the configuration space (the positions of all the particles) is divided into regions where the corresponding value of the wave function is positive and regions where the corresponding value wave function is negative ('nodal pockets'). The positive and negative regions must clearly be separated by a 3N-1 dimensional hypersurface where the wave function is zero and across which it changes sign (the 'nodal surface').

    This applied as much for the 'wave function of the universe' (where N is the number of particles in the universe) as it does to the wave function of an isolated subsystem.
     
  7. Nov 2, 2009 #6
    Re: Does the wavefunction have a zero value anywhere??

    I didn't understand much of what you said, but thanks for the answer
     
  8. Nov 2, 2009 #7
    Re: Does the wavefunction have a zero value anywhere??

    Sorry - I'll repeat in human language:

    In some places the wave function is positive. In some other places it is negative. By definition, in passing from positive to negative you have to go through a surface on which it is zero. Hence there are a very large number of places in which the wave function is zero.

    (If I might be permitted to get all complicated on your ***: remember also that the wave function is a function of the positions of all the particles i.e. we write it as Psi(x_1,x_2,...x_N) - the technical way of saying this is that it is defined on a configuration space. So when I say 'place' I mean a 'place in configuration space' i.e. a list of the positions of all the particles).

    Edit: I can't believe the software asterisks out the word *** - I mean, are we all children around here?
     
    Last edited: Nov 2, 2009
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