Question

WKB expression for Dirac equation?

Answer 1

given the one dimensional Schroedinger equation

−ℏ22md2dx2Ψ(x)+V(x)Ψ(x)=EnΨ(x)

the WKB method for the energies is

(n+1)2πℏ=∫baEn−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

(βmc2+∑k=13αkpkc)ψ(x,t)+V(x)Ψ(x,t)=iℏ∂ψ(x,t)∂t

Answer 2

formula is
$\beta \gamma 45 \tan( \cot(12hii) ) 000\% log_{ \sec(454) }(2323232) ooo$