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The uncertainty operator and Heisenberg

  1. Feb 26, 2014 #1

    dyn

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    In deriving the Heisenberg uncertainty relation for 2 general Hermitian operators A and B , the uncertainty operators ΔA and ΔB are introduced defined by ΔA=A - (expectation value of A) and similarly for B.
    My question is this - how can you subtract(or add) an expectation value , which is just a number to A which is an operator ?
     
  2. jcsd
  3. Feb 26, 2014 #2

    atyy

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    A number is also an operator. But you can also see it by the variance being <A.A>-<A>2, where <A.A> is a number and <A> is a number.

    <(A-<A>)2>
    = <A.A-2<A>A+<A>2>
    = <A.A>-<2<A>A>+<<A>2>
    = <A.A>-2<A><A>+<<A>2>
    = <A.A>-<A>2
     
  4. Feb 26, 2014 #3

    WannabeNewton

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    There's an implicit identity operator multiplying ##\langle A \rangle##.
     
  5. Feb 27, 2014 #4

    dextercioby

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    That's sloppy and indeed misleading notation. The unit operator on the states' space is not written when scaled by the expectation value.
     
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