Toru Miyazawa

We study low-energy expansion and high-energy expansion of reflection coefficients for one-dimensional Schrödinger equation, from which expansions of the Green function can be obtained. Making use of the equivalent Fokker-Planck equation, we develop a generalized formulation of a method for deriving these expansions in a unified manner. In this formalism, the underlying algebraic structure of the problem can be clearly understood, and the basic formulas necessary for the expansions can be derived in a natural way. We also examine the validity of the expansions for various asymptotic behaviors of the potential at spatial infinity.

We study low-energy expansion and high-energy expansion of reflection coefficients for one-dimensional Schrodinger equation, from which expansions of the Green function can be obtained. Making use of the equivalent Fokker-Planck equation, we develop a generalized formulation of a method for deriving these expansions in a unified manner. In this formalism, the underlying algebraic structure of the problem can be clearly understood, and the basic formulas necessary for the expansions can be derived in a natural way. We also examine the validity of the expansions for various asymptotic behaviors of the potential at spatial infinity. (C) 2015 AIP Publishing LLC.

We study the low-energy behavior of the Green function for one-dimensional Fokker-Planck and Schrodinger 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.