Little issue with relativistic quantum mechanics

1. Sep 9, 2015

StephvsEinst

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. Sep 9, 2015

Orodruin

Staff Emeritus
The i is not there in the momentum space version of the Dirac equation. Wherever you took this from has a typo.

3. Sep 10, 2015

StephvsEinst

Thanks for the answer. So I did it correctly?