1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Hermitian operator

  1. May 22, 2008 #1
    How do I show that an arbitrary operator A can be writte as A = B + iC where B and C are hermitian?
  2. jcsd
  3. May 22, 2008 #2
    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
  4. May 22, 2008 #3


    User Avatar
    Science Advisor
    Homework Helper

    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?