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Inverse Operator

  1. May 6, 2008 #1
    hello,

    given is the Operator L=[tex]\widehat{1}[/tex]+|u><v|, where [tex]\widehat{1}[/tex] means the unity-tensor.

    Whats the inverse of L?

    I calculated the inverse of L in R^2 but I dont get it back to the bra-ket-notation. Can somebody help?


    BTW: Sorry for my bad english!
     
  2. jcsd
  3. May 6, 2008 #2
    The inverse of this operator, assuming <u|v>=0, that is orthogonality, is given by 1-|u><v|.

    When in doubt about this matter put

    [tex]L^{-1}=a\widehat{1}+b|u><v|[/tex]

    and using [tex]LL^{-1}=L^{-1}L=\widehat{1}[/tex] fix coeficients a and b. This is a general strategy for this kind of algebraic manipulations.


    Jon
     
    Last edited: May 6, 2008
  4. May 6, 2008 #3
    Thx for your fast answer!

    I think a had already that kind of inverse operator, but I didn't assume that <u|v>=0. :shy:

    Tobi
     
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