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 operators

  1. Oct 26, 2006 #1

    [tex]\mathcal{L} = \frac{d}{dx} p(x) \frac{d}{dx} + q(x)[/tex]

    be a self-adjoint operator on functions [tex]f : [a,b] \rightarrow \mathbb{C}[/tex]. Under what circumstances is the operator Hermitian with

    [tex]<u|v> = \int_a^b u^*(x) v(x) dx[/tex]

    Can someone give me a hint on this one? I know that hermitian operators satisfies

    [tex]<u|\mathcal{L}v> = <\mathcal{L}u|v>[/tex]

    but I don't really get the question.
    Last edited: Oct 26, 2006
  2. jcsd
  3. Oct 26, 2006 #2


    User Avatar
    Science Advisor
    Homework Helper

    My guess is it is something very close to what is done here.


    What does [tex]f : [a,b] \rightarrow \mathbb{C}[/tex] mean? Is this a completeness condition?
  4. Oct 26, 2006 #3
    Not a completeness condition, just specifying the domain (from a to b) and the range (complex numbers)...

    But as for the question, since you know the Hermitian condition, plug in your actual operator L and then simplify both sides, possibly integrating by parts to shift derivatives around. Then, when you have the two sides looking somewhat similar, you should be able to come up with conditions under which the two sides are equal.

    (Yeah, I know that's kind of vague, but it should get you started...)
  5. Oct 26, 2006 #4


    User Avatar
    Science Advisor
    Homework Helper

    Thanks. I always was weak on those funny letter math symbols :rolleyes:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Hermitian operators
  1. Hermitian Operators? (Replies: 6)

  2. Hermitian operator (Replies: 10)

  3. Hermitian Operators (Replies: 5)

  4. Hermitian Operators (Replies: 15)