Low-energy asymptotic expansion of the Green function for one-dimensional Fokker-Planck and Schr\"odinger equations

We consider Schr"odinger equations and Fokker-Planck equations in one dimension, and study the low-energy asymptotic behavior of the Green function using a new method. In this method, the coefficient of the expansion in powers of the wave number can be systematically calculated to arbitrary order, and the behavior of the remainder term can be analyzed on the basis of an expression in terms of transmission and reflection coefficients.