Hermitian operator

  • Thread starter Dragonfall
  • Start date
  • #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?
 

Answers and Replies

  • #2
705
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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?
 
Last edited:
  • #3
mathwonk
Science Advisor
Homework Helper
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anytime anywhere you have an involution J you can alwaYS WRiTE ANYTHIng AS

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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