Low-energy expansion formula for one-dimensional Fokker-Planck and   Schr\"odinger equations with periodic potentials
  We study the low-energy behavior of the Green function for one-dimensional Fokker-Planck and Schr\"odinger 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. 
Toru Miyazawa
math-ph cond-mat.stat-mech math.MP quant-ph