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arXiv · 1505.03298

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

Toru Miyazawa
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Abstract

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.

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Toru Miyazawa. 2015-05-13. Formulation of a unified method for low- and high-energy expansions in the analysis of reflection coefficients for one-dimensional Schrödinger equation. https://doi.org/10.1063/1.4918552

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