How do I show that an arbitrary operator A can be writte as A = B + iC where B and C are hermitian?
May 22, 2008 #1 Dragonfall 1,030 4 How do I show that an arbitrary operator A can be writte as A = B + iC where B and C are hermitian?
May 22, 2008 #2 Edgardo 705 15 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: May 22, 2008
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?
May 22, 2008 #3 mathwonk Science Advisor Homework Helper 11,464 1,717 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.
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.