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Does a position operator exist?

  1. Sep 1, 2009 #1
    Does a position operator exist?
     
  2. jcsd
  3. Sep 1, 2009 #2

    Pengwuino

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    Re: Eigenfunction

    What do you mean exist? I don't want to just blurt out "yes" to such a seemingly obvious question...
     
  4. Sep 1, 2009 #3
    Re: Eigenfunction

    Does a position operator acting on a wavefunction give a position eignenfunction?
     
  5. Sep 1, 2009 #4

    Pengwuino

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    Re: Eigenfunction

    Yes, if the wavefunctions are eigenfunctions of the position operator ;)
     
  6. Sep 1, 2009 #5
    Re: Eigenfunction

    For the correct wavefunction (Dirac delta function), yes. For other wavefunctions, no.
     
  7. Sep 1, 2009 #6
    Re: Eigenfunction

     
  8. Sep 1, 2009 #7

    Pengwuino

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    Re: Eigenfunction

    No... why would it?
     
  9. Sep 1, 2009 #8
    Re: Eigenfunction

     
  10. Sep 2, 2009 #9
    Re: Eigenfunction

    No, the momentum operator does not collapse the wavefunction.

    You just get a new wavefunction [tex]F'=p_{1}0.8a+p_{2}0.6b[/tex]. (And you'd still have to normalize that.)
     
  11. Sep 2, 2009 #10
    Re: Eigenfunction

    Mathematically that is what you get when you apply the momentum operator to the wavefunction F. However, I was actually thinking about physically measuring the momentum of the wavefunction, in which the wavefunction then collapses into a or b. So my quesiton is then, when the position of a wavefunction is measured, will the wavefunction likewise collapse into a position eigenfunction just as it would if it was a momentum measurement.
     
  12. Sep 2, 2009 #11
    Re: Eigenfunction

    In principle it would, but unless it's trapped in an infinitely deep and infinitesimally narrow potential well, that eigenfunction won't be a stationary state, and will immediately evolve into something else. A wavefunction corresponding to an exactly defined position you would also have infinite uncertainty in momentum.

    Essentially it would require a potential resembling the limiting case of an infinite square well, where the length of the well approaches zero.
     
  13. Sep 4, 2009 #12
    Re: Eigenfunction

     
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