WKB asymptotics of meromorphic solutions of difference equations

2019/03/05 by Alexander Fedotov, Frédéric Klopp, Fedotov, Alexander +1 · 1 citation
Physics and Astronomy · Mathematics · #Quantum chaos and dynamical systems #Quantum Mechanics and Non-Hermitian Physics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1903.02224

Abstract

We consider the difference Schr''odinger equation ψ(z+h)+ψ(z-h)+ v(z)ψ(z)=0 where z is a complex variable and h is a small positive parameter. If 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. In the present paper, we assume that v has a simple pole and, in its neighborhood, we study the asymptotics of meromorphic solutions to the difference Schr''odinger equation.

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