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How do I show that an arbitrary operator A can be writte as A = B + iC where B and C are hermitian?

- Thread starter Dragonfall
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- #1

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How do I show that an arbitrary operator A can be writte as A = B + iC where B and C are hermitian?

- #2

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Rewrite A as follows:

[tex]A = \frac{(A+A^{\dagger})}{2} + \frac{(A-A^{\dagger})}{2}[/tex]

Do you see why you can write A like that?

And can you carry on?

[tex]A = \frac{(A+A^{\dagger})}{2} + \frac{(A-A^{\dagger})}{2}[/tex]

Do you see why you can write A like that?

And can you carry on?

Last edited:

- #3

mathwonk

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x = (x+JX)/2 + (X-JX)/2,

where X+JX is invariant under J, and X-JX is anti-invariant under J.

this is what lies beneath this fact.

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