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Bras and Kets

  1. Jul 26, 2005 #1
    I am trying to show that |g> = A|f> implies
    <g| = <f|B

    where A is an operator and B is its Hermitian conjugate.
    I think my problem is with notation, but i have not been able to show this as yet.

  2. jcsd
  3. Jul 26, 2005 #2


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    In a matrix representation, you can write the original equation as a sum of products using matrix multiplication rules. Take the complex conjugate, and replace the conjugates of the elements of A with elements of B. Then from the relationship between elements of <g| and |g>, <f| and |f> you have all you need.
  4. Jul 26, 2005 #3


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    That's pretty much the definition of Hermitian conjugate, isn't it?
  5. Jul 26, 2005 #4


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    As far as I'm aware, that is how the hermitian conjugate (or adjoint) is defined - though the dual correspondence for A|a> !

    I guess you could take the matrix operation of finding the adjoint as definition, and "derive" this result as Older Dan suggests.
  6. Jul 27, 2005 #5
    We have only just been introduced to Dirac notation, and have not had a lot of experience in linear analysis and dual vector spaces etc... I have figured out how to do it, i just contract |g> with an arbitrary bra <h|, then do the same with <g| and an arbitrary bra |h>, show the two are equal and hence the expression for <g| must be correct.
    Thanks for the help guys, much appreciated
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