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A question on the Aharonov-Bohm effect

  1. Oct 4, 2011 #1
    We know that Aharonov-Bohm effect is explained by quantum theory.

    But, I imagine the situation that the solenoid is very far from two-slit.
    In this case, does Aharonov-Bohm effect happen?

    Current quantum theory doesn't consider the distance between two-slit and the solenoid.
    When the distance two-slit and the solenoid becomes larger, Aharonov-Bohm effect disappears or continues?
     
    Last edited: Oct 4, 2011
  2. jcsd
  3. Oct 5, 2011 #2

    Matterwave

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    The solenoid must be enclosed by the 2 paths in order for there to be an effect. If the 2 paths does not enclose the solenoid, then no such effect would be present, even quantum mechanically.
     
  4. Oct 5, 2011 #3
    MatterWave
    I think that the solenoid is enclosed by the 2 paths even if that is far from two-slit.
    Quantum mechanics doesn't say that the solenoid is not enclosed although solenoid is far from two-slit.
    What kind of QM books or quantum theorists say like your opinion?
    I want to know what your opinion is based on.
     
  5. Oct 5, 2011 #4

    Matterwave

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    The Ahronov-Bohm effect says that for a 2 slit experiment, if the particle "travels" on 2 possible paths to the end point, then there is a relative shift in phase between the 2 even if the path lengths are the same because of this solenoid. This relative phase shift is proportional to the flux of the magnetic field going through the surface which is enclosed by the 2 paths. If you move your solenoid "far away" outside of these two paths, you obviously have no magnetic flux going through this surface (neglecting fringe effects of course), and therefore no relative phase shift.
     
  6. Oct 5, 2011 #5
    Matterwave
    You misunderstand Quantum mechanics.
    You say "If you move your solenoid "far away" outside of these two paths..."
    But, the solenoid can be in these two paths. You can draw the two paths which include the the solenoid.
    How about that case?
    You think only the case that the solenoid is outside of the two pathes.
     
  7. Oct 5, 2011 #6

    Matterwave

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    The contribution to the interference is mainly from the 2 straight paths (the light rays). The paths you have to draw to include this solenoid far away do not contribute much to the interference pattern.
     
  8. Oct 5, 2011 #7
    Matterwave
    2 straight paths?
    I don't see what you say in QM book. Many QM books don't say about the shape of pathes. I can't believe what you say is true.
     
  9. Oct 5, 2011 #8

    Matterwave

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    How do you usually describe 2 slit interference?
     
  10. Oct 5, 2011 #9

    Matterwave

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    If you want a reference, you can read Gottfried and Yan's Quantum Mechanics Fundamentals Page 196. They tell you there that the main contributions to the interference is due to the classical (straight-line) paths and their close neighbors.
     
  11. Oct 5, 2011 #10
    Thank you
     
  12. Oct 5, 2011 #11
    Matterwave
    Thank you for discussing this subject and saying me something useful.
    I want to talk to you with the other quantum mechanical problem.
    If you see this comment, contact me. mrhun@hanmail.net
     
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