# Dirac equation boundary conditions

In Schroedinger equation, which is second order differential equation, one normally, equates both $$\psi(x)$$ and $$\psi'(x)$$ across the boundary, as boundary conditions. However, the dirac equation is a first order differential equation. So, if one were to have a dirac equation like $$\gamma^{\mu}\partial_{\mu}\psi -m\psi + V(x)\psi = 0,$$ where lets say $$V(x)$$ is a potential barrier, would one require to equate both $$\psi$$ and $$\psi'$$ as boundary conditions? Since Dirac equation is a 1st order differential equation, mathematically, is seems only $$\psi(x)$$ needs to be equated across the boundary. Also, since Dirac equation is a matrix equation, equating both $$\psi(x)$$ and $$\psi'(x)$$ would lead to over constraining the system; and rendering it unsolvable.

Another point of confusion on this is that a particle satisfying Dirac equation would satisfy klein gordon equation which is a second order differential equation.