The complex WKB method for difference equations and Airy functions

Frédéric Klopp, Alexander Fedotov

We consider the difference Schr{ö}dinger equation $\psi$(z + h) + $\psi$(z -- h) + v(z)$\psi$(z) = 0 where z is a complex variable, h > 0 is a parameter, and v is an analytic function. As h…