Inverse Operator

  • Thread starter Bimmel
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  • #1
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Main Question or Discussion Point

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!
 

Answers and Replies

  • #2
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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:
  • #3
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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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