given the one dimensional Schroedinger equation
$$ - \frac{\hbar ^{2}}{2m} \frac{d^{2}}{dx^{2}}\Psi(x)+ V(x) \Psi(x) =E_{n}\Psi (x) $$
the WKB method for the energies is $$ (n+1)2\pi \hbar =\int_{a}^{b}\sqrt{E_{n}-V(x)}dx$$
with 'a' and 'b' being turning points
my question is what is the WKB aproximation for the Dirac equation in one or two dimension
$$ \left(\beta mc^2 + \sum_{k = 1}^3 \alpha_k p_k \, c\right) \psi (\mathbf{x},t)+V(x)\Psi(x,t) = i \hbar \frac{\partial\psi(\mathbf{x},t) }{\partial t} $$
