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Derivation of Uncertainty Princple

  1. Jun 17, 2009 #1
    Referrence to Modern Quantum Mechanics, J.J.Sakurai,
    I found the "Generalized Uncertainty Principle" is that
    <( s.d. of operator A)^2> <( s.d. of operator B)^2> >= 1/4 |<[A,B]>|^2 + 1/4 |<{s.d of A, s.d of B}>|^2

    I hope it is not difficult to read, as I don't know how to type it formally.
    I would like to ask why the inequality finally omitted the second (the anticommutator) term ?
    Sakurai said it is because the second term can only make the inequality relation stronger.
    I can't understand. Besides, I am a UG Year 1 students, but familiar to Dirac Notation as I am doing UG research on Quantum Information Theory. I hope any one can explain it in a easy way ^^ Thank You
  2. jcsd
  3. Jun 17, 2009 #2


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    The second term is always positive. Therefore if LHS >= First + Second, LHS >= First will always be true. And omitting the second term makes the uncertainty principle look "nicer".
  4. Jun 17, 2009 #3


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    Hi ChrisLM! :smile:

    oooh, nicksauce :smile: has beat me to it!

    anyway, have a geq: ≥, and try using the X2 tag just above the Reply box :wink:)
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