Complex WKB method for a difference Schrödinger equation with the potential being a trigonometric polynomial

DOI10.1090/SPMJ/1497zbMath1385.39001OpenAlexW2791430464MaRDI QIDQ4608712

Alexander Fedotov, E. Shchetka

Publication date: 22 March 2018

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/spmj/1497

zbMATH Keywords

asymptoticscomplex WKB methodentire solutionsdifference Schrödinger equation

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Discrete version of topics in analysis (39A12) Growth, boundedness, comparison of solutions to difference equations (39A22)

Related Items (14)

Complex WKB method for a system of two linear difference equations ⋮ Plancherel–Rotach type asymptotic formulae for multiple orthogonal Hermite polynomials and recurrence relations ⋮ Uniform asymptotic solution in the form of an Airy function for semiclassical bound states in one-dimensional and radially symmetric problems ⋮ Close turning points and the Harper operator ⋮ Complex WKB method (one-dimensional linear problems on the complex plane) ⋮ Semiclassical asymptotics of transition matrices for difference equations with two coalescing turning points ⋮ On the hierarchical behavior of solutions of the Maryland equation in the semiclassical approximation ⋮ Lagrangian manifolds related to the asymptotics of Hermite polynomials ⋮ Semiclassical asymptotics for a difference Schrödinger equation with two coalescent turning points ⋮ An approach to finding the asymptotics of polynomials given by recurrence relations ⋮ WKB asymptotics of meromorphic solutions to difference equations ⋮ The Complex WKB Method for Difference Equations and Airy Functions ⋮ Averaging and spectral bands for the 2-D magnetic Schrödinger operator with growing and one-direction periodic potential ⋮ Difference equations in the complex plane: quasiclassical asymptotics and Berry phase

Cites Work

• The complex WKB method for difference equations in bounded domains
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Complex WKB method for a difference Schrödinger equation with the potential being a trigonometric polynomial