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.
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.