%0 Journal Article
%T Formulation of a unified method for low- and high-energy expansions in the analysis of reflection coefficients for one-dimensional Schr£żdinger equation
%A Toru Miyazawa
%J Physics
%D 2015
%I arXiv
%R 10.1063/1.4918552
%X We study low-energy expansion and high-energy expansion of reflection coefficients for one-dimensional Schr\"odinger 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.
%U http://arxiv.org/abs/1505.03298v1