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I Is this number real?

  1. Dec 22, 2017 #1

    dyn

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    hi. I have been looking at a QM example in a book. It works out the expectation value for momentum which I know should be a real number but I can't see how or why the following number is real
    α and β are complex numbers with | α |2 + | β |2 = 1 and ω and t are real

    -i ( α*β e-iωt -αβ*eiωt)

    Can anyone tell me if this is a real number and why?
    Thanks
     
  2. jcsd
  3. Dec 22, 2017 #2

    mfb

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    2017 Award

    Staff: Mentor

    The two parts in the bracket are the complex conjugates of each other: They have the same real component but opposite imaginary component. Their difference has a real component of zero, it is purely imaginary. If you multiply that by -i you get a real number.
     
  4. Dec 23, 2017 #3

    dyn

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    Thanks. I just couldn't see it but now I can. Thanks again
     
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