Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Can diffraction be explained by quantisation?

  1. May 11, 2016 #1
    I was wondering if the diffraction pattern through a single slit could be explained as a consequence of quantisation of momentum transverse to the main direction of travel. I know that momentum gets quantised on confinement so does the confinement in a slit quantise the momentum so that only certain final directions of the particle are likely?
     
  2. jcsd
  3. May 11, 2016 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Not directly, as you don't establish a standing wave in your slit. The concepts are related, of course, and the momentum distribution afterwards is the Fourier transformation of the slit pattern (for small angles, and up to constants).
     
  4. May 11, 2016 #3

    Vanadium 50

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor

    You can also get diffraction with purely classical water waves.
     
  5. May 11, 2016 #4
    Why is it different to a potential well? Is there just not enough time for a standing wave to establish?
     
  6. May 12, 2016 #5

    bhobba

    User Avatar
    Science Advisor
    Gold Member

    It is a consequence of the uncertainty relations:
    http://cds.cern.ch/record/1024152/files/0703126.pdf

    Thanks
    Bill
     
  7. May 12, 2016 #6
    Wow that is a great QM education article for learners.

    Printed.

    Thanks for posting.
     
  8. May 12, 2016 #7
    The author's approach isn't one generally encountered, so thanks for posting it. In the single slit there is obviously a change in the transerve momentum of the particle. How is the momentum conserved? Does the the particle start bouncing around between the sides of the well?
     
  9. May 12, 2016 #8

    bhobba

    User Avatar
    Science Advisor
    Gold Member

    Momentum is not conserved - it is changed by the observation. It does not bounce around.

    Thanks
    Bill
     
  10. May 12, 2016 #9
    I thought momentum was always conserved. Doesnt the confinement introduce the uncertainty into the momentum rather than the observation?
     
  11. May 13, 2016 #10
    Confinement times momentum = constant = Heisenberg UP.
     
  12. May 13, 2016 #11

    bhobba

    User Avatar
    Science Advisor
    Gold Member

    In QM it isn't because of the HUP. By Ehrenfests theorem its conserved on the average. The uncertainty is introduced by the fact going through a slit means just behind the slit it's position is very certain so by the HUP its momentum is unknown. But since KE is conserved this means its velocity is unchanged so it's direction is uncertain. That's why you get a diffraction pattern.

    Thanks
    Bill
     
  13. May 13, 2016 #12

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Momentum is conserved exactly in every interaction. Your measurement system will provide any apparent change of momentum, and you rarely care about the momentum of the system, so it looks like your momentum changed. But total momentum was always constant.
     
  14. May 13, 2016 #13

    bhobba

    User Avatar
    Science Advisor
    Gold Member

    Hmmm. Good point.

    Thanks
    Bill
     
  15. May 13, 2016 #14
    Are you saying that it's the measuring device rather than the slit that provides the means of compensating for the momentum change?
     
  16. May 14, 2016 #15

    vanhees71

    User Avatar
    Science Advisor
    2016 Award

    No, there's an interaction of the particles with the material making up the slits and thus the particles that hit this material transfer momentum to it. Of course, for any closed system momentum is conserved, but particles interacting with the material are not a closed system. The usual treatment of course hides the microscopic picture by just imposing semiclassical boundary conditions, which is an effective description of the very complicated microscopic interactions, and it's accurate enough to understand the measured pattern on the screen. In Fraunhofer observation you get (as in the Kirchhoff approximation of diffraction in classical optics) just the Fourier transform of the slits (e.g., a sinc function for the single slit).
     
  17. May 14, 2016 #16
    So there is something akin to bouncing going on and it would seem that some transfers of momentum are more likely than others.
     
  18. May 14, 2016 #17

    bhobba

    User Avatar
    Science Advisor
    Gold Member

    How you draw that conclusion I can't follow.

    Its as I said, and the link I gave said, due to the uncertainty relations the momentum is uncertain - in fact any value is equally likely - see equation 8. The particle is not a closed system so its momentum can change, although as MFB correctly pointed out in the interaction overall momentum must be conserved.

    Thanks
    Bill
     
  19. May 14, 2016 #18
    My original question pertained to the diffraction pattern. Equation 8 appears only applicable to the infinitesimally narrow slit. Please see equation 18.
     
  20. May 14, 2016 #19

    bhobba

    User Avatar
    Science Advisor
    Gold Member

    Your point being?

    It uses the infinitesimal slit to derive the finite one.

    Thanks
    Bill
     
  21. May 14, 2016 #20
    The point being that some changes in momentum are more likely than others.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Can diffraction be explained by quantisation?
Loading...