Abstract
We consider the difference Schrödinger equation where z is a complex variable, E is a spectral parameter, and h is a small positive parameter. If the potential v is an analytic function, then, for h sufficiently small, the analytic solutions to this equation have standard semi-classical behavior that can be described by means of an analog of the complex WKB method for differential equations. We assume that v has a simple pole and, in its neighborhood, we study the asymptotics of meromorphic solutions to the difference Schrödinger equation.
Disclosure statement
No potential conflict of interest was reported by the authors.
ORCID
Alexander Fedotov http://orcid.org/0000-0002-8010-3004