WKB asymptotics of meromorphic solutions to difference equations. Issue 7 (19th May 2021)

• Record Type: Journal Article
• Authors: Fedotov, Alexander; Klopp, Frédéric
• Is Part Of: Applicable analysis. Volume 100:Issue 7(2021)
• Page Start: 1557
• Page End: 1573
• Publication Date: 2021-05-19
• Subjects: Semiclassical asymptotics -- complex WKB method -- difference equations -- meromorphic coefficients; 34M60 -- 39A45; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1652735
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : We consider the difference Schrödinger equation ψ ( z + h ) + ψ ( z − h ) + v ( z ) ψ ( z ) = E ψ ( z ) 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.