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

Abstract

We study the low-energy behavior of the Green function for one-dimensional Fokker-Planck and Schrödinger equations with periodic potentials. We derive a formula for the power series expansion of reflection coefficients in terms of the wave number, and apply it to the low-energy expansion of the Green function.

References in corpus (3)

• On the Cauchy Problem for the Korteweg-de Vries Equation with Steplike Finite-Gap Initial Data I. Schwartz-Type Perturbations
• 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

Cited by in corpus (2)

• Formulation of a unified method for low- and high-energy expansions in the analysis of reflection coefficients for one-dimensional Schrödinger equation
• Low-energy expansion formula for one-dimensional Fokker-Planck and Schrödinger equations with asymptotically periodic potentials