# Clarification of spinor solutions in Srednicki

1. Feb 16, 2016

### Higgsy

On page 235 of srednicki (print) it says to plug a solution of the form $$\textbf{\Psi} (x) = u(\textbf{p})e^{ipx} + v(\textbf{p})e^{-ipx}$$ into the dirac equation $$(-i\gamma^{\mu} \partial_{\mu}+m)\textbf{\Psi}=0$$

To get

$$(p_{\mu}\gamma^{\mu} + m)u(\textbf{p})e^{ipx} + (-p_{\mu}\gamma^{\mu} + m)v(\textbf{p})e^{-ipx} = 0$$

I'm wondering what the reasoning for this term is (not wrt negative or positive but simply why p) $$p_{\mu}\gamma^{\mu}$$

2. Feb 16, 2016

### Orodruin

Staff Emeritus
Did you try just plugging it into the Dirac equation? What did you get?