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Abstract <p> We study a one-dimensional Schrödinger equation on the positive semiaxis with a potential equal to the sum of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\delta\)</EquationSource> </InlineEquation>-functions such that the distances between their supports increase linearly with the distance from the origin. Studying the behavior of its solutions at infinity is reduced to studying solutions of a difference equation with self-similar properties. </p>

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On a Schrödinger Equation with Potential Barriers the Distances between Which Increase

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • N. I. Andronov,
  • A. A. Fedotov

摘要

Abstract

We study a one-dimensional Schrödinger equation on the positive semiaxis with a potential equal to the sum of \(\delta\) -functions such that the distances between their supports increase linearly with the distance from the origin. Studying the behavior of its solutions at infinity is reduced to studying solutions of a difference equation with self-similar properties.