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Hesienberg Uncertanity Principle

  1. Aug 16, 2014 #1
    I watched a video about particle physics and there I saw something strange(for me) (link is here) and there in 13:44 I saw [x,y] I didnt understand because I think uncertanity principle exist only between position and momentum but he make uncertanity between two coordinates .Can somebody explain to me how [x,y] works.

    Thanks
     
    Last edited by a moderator: Sep 25, 2014
  2. jcsd
  3. Aug 16, 2014 #2

    tom.stoer

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    He explicitly writes

    [tex][x,y] = 0[/tex]
    [tex][p_x,p_y] = 0[/tex]

    So the uncertainty relation for x and y will read

    [tex]\Delta x \; \Delta y = 0[/tex]

    Then he discusses the commutator for angular momentum.

    [tex][L_x,L_y] \neq 0[/tex]

    and from that one can derive an uncertainty relation for angular momentum.
     
  4. Aug 16, 2014 #3
    so theres no problem
     
  5. Aug 16, 2014 #4

    tom.stoer

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    no, there isn't
     
  6. Aug 16, 2014 #5
    thanks
     
  7. Aug 18, 2014 #6
    The expression [x, y] is called the commutator of x and y
    http://en.wikipedia.org/wiki/Commutator

    As you may know it's defined as [x, y] = xy - yx where x and y are any two operators. There's an uncertainty relation for any two observables A and B since [A,B] are what appear in the right hand side and the standard deviations of A and B appear on the left side of the inequality (uncertainty in Q = standard deviation in Q).
     
    Last edited by a moderator: Sep 25, 2014
  8. Aug 18, 2014 #7
    An uncertainly relation holds between any two non-commuting observables.
     
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