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Dirac ket-bra simplification over here.

  1. Apr 5, 2014 #1
    I usually know how to manipulate bras and kets. But I probably found difficulty because of the double summation. How did Sakurai manage to go from the second line to the ird line in the attachment?

    SECTION 4.4 in Sakurai.
     

    Attached Files:

  2. jcsd
  3. Apr 5, 2014 #2
    Using the orthogonality condition
     
    Last edited: Apr 5, 2014
  4. Apr 5, 2014 #3

    Bill_K

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    Along with UU = I.
     
  5. Apr 6, 2014 #4
    How come? If so I will end up with a zero, no?
     
  6. Apr 6, 2014 #5
    I was thinking about taking duality but that didn't seem to work.
     
  7. Apr 6, 2014 #6

    kith

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    No. What is [itex]\langle a''|a' \rangle[/itex] equal to and what does this imply for [itex] \Sigma_{a''} \langle a''|a' \rangle[/itex]?
     
  8. Apr 6, 2014 #7
    It is equal to 1 if a=a'' and 0 otherwise if we take orthogonality into consideration.. It implies that the summation = 1 when a'' = a' and 0 for all the other summations. Right?
     
  9. Apr 6, 2014 #8

    kith

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    Yes. If you put Bill's comment and this together, do you still miss something to go from line two to line three?
     
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