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

Little issue with relativistic quantum mechanics

  1. Sep 9, 2015 #1
    Hey!

    I was working with Dirac's equation:
    $$ ( i \hbar \gamma^\mu \partial_\mu - m ) \psi = 0, $$
    and I found that if you work with a function that depends on the momentum, $$ \psi ( \mathbf{p} ), $$ you obtain:
    $$ ( i \gamma \cdot \mathbf{p} + m ) \psi ( \mathbf{p} ) = 0. $$
    The problem is that I can't figure out how did the imaginary number not disappear in the last equation. I tried to work with $$ p_\mu \rightarrow i \hbar \partial_\mu , $$
    and I obtained the following:
    $$ ( \gamma \cdot \mathbf{p} + m ) \psi ( \mathbf{p} ) = 0. $$
    Help?
    $$ --- $$
    The $$ \gamma $$ are the Gell-Mann marices.
     
  2. jcsd
  3. Sep 9, 2015 #2

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    The i is not there in the momentum space version of the Dirac equation. Wherever you took this from has a typo.
     
  4. Sep 10, 2015 #3
    Thanks for the answer. So I did it correctly?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Little issue with relativistic quantum mechanics
Loading...