# WKB expression for Dirac equation?

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

$$\left(\beta mc^2 + \sum_{k = 1}^3 \alpha_k p_k \, c\right) \psi (\mathbf{x},t)+V(x)\Psi(x,t) = i \hbar \frac{\partial\psi(\mathbf{x},t) }{\partial t}$$

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