- #1

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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.

Thanks

Ray

- Thread starter rayveldkamp
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- #1

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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.

Thanks

Ray

- #2

OlderDan

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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.rayveldkamp said:

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.

Thanks

Ray

- #3

HallsofIvy

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That's pretty much therayveldkamp said:

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.

Thanks

Ray

- #4

Gokul43201

Staff Emeritus

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As far as I'm aware, thatHallsofIvy said:That's pretty much thedefinitionof Hermitian conjugate, isn't it?

I guess you

- #5

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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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