Formulation of a unified method for low- and high-energy expansions in the analysis of reflection coefficients for one-dimensional Schr\"odinger equation

@article{Miyazawa2015FormulationOA,
  title={Formulation of a unified method for low- and high-energy expansions in the analysis of reflection coefficients for one-dimensional Schr\"odinger equation},
  author={Toru Miyazawa},
  journal={arXiv: Mathematical Physics},
  year={2015}
}
  • T. Miyazawa
  • Published 13 May 2015
  • Mathematics
  • arXiv: Mathematical Physics
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… 
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