Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Hermitian operators

  1. Nov 14, 2016 #1
    In the dirac equation we have a term which is proportional to [tex] \alpha p [/tex]. In the book they say that
    [tex] \alpha [/tex] must be an hermitian operator in order for the Hamiltonian to be hermitian.

    As I understand, we require this because we want [tex] (\alpha p)^\dagger = \alpha p[/tex].

    But [tex] (\alpha p)^\dagger = p^\dagger \alpha^\dagger = p \alpha [/tex], and so the order of the operators still change.

    So if we just require both operators to be hermitian their product will still change if we take the hermitian conjugate.
    Last edited by a moderator: Nov 15, 2016
  2. jcsd
  3. Nov 14, 2016 #2


    User Avatar
    Science Advisor
    Homework Helper

    ##p## acts on spatial part whereas ##\alpha## on spin part so the two operators commute.
  4. Nov 14, 2016 #3
    ok, thanks!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted