Low-energy expansion formula for one-dimensional Fokker-Planck and Schrödinger equations with asymptotically periodic potentials

Abstract

We consider one-dimensional Fokker-Planck and Schrödinger equations with a potential which approaches a periodic function at spatial infinity. We extend the low-energy expansion method, which was introduced in previous papers, to be applicable to such asymptotically periodic cases. Using this method, we study the low-energy behavior of the Green function.

arXiv commentauthor-created, un-copyedited version of an article accepted for publication in Journal of Physics A: Mathematical and Theoretical

References in corpus (4)

• Scattering Theory for Jacobi Operators with Quasi-Periodic Background
• Analysis of reflection coefficients for the Fokker-Planck equation
• Low-energy asymptotic expansion of the Green function for one-dimensional Fokker-Planck and Schrödinger equations
• Low-energy expansion formula for one-dimensional Fokker-Planck and Schrödinger equations with periodic potentials

Cited by in corpus (1)

• Formulation of a unified method for low- and high-energy expansions in the analysis of reflection coefficients for one-dimensional Schrödinger equation