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<p>In this paper, we consider the inverse scattering problem for one-dimensional Schr<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\ddot{o}\)</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mi>o</mi> <mo>¨</mo> </mover> </math></EquationSource> </InlineEquation>dinger operator on the half-line <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\([0,\infty )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mi>∞</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> with spectral parameter dependent on boundary condition and interior discontinuous conditions. The scattering data of the problem is defined and the modified Marchenko main equation is derived. With the help of the obtained integral equations, it is shown that the potential is uniquely recovered by the given scattering data.</p>

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Inverse scattering problems for discontinuous Schrodinger operators with spectral parameter dependent on boundary condition

  • 期刊论文

  • 发表日期：

    2025年12月14日

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  • Lu Zhou,
  • Yongxia Guo,
  • Yanyan Tian,
  • Guangsheng Wei

摘要

In this paper, we consider the inverse scattering problem for one-dimensional Schr \(\ddot{o}\) o ¨ dinger operator on the half-line \([0,\infty )\) [ 0 , ∞ ) with spectral parameter dependent on boundary condition and interior discontinuous conditions. The scattering data of the problem is defined and the modified Marchenko main equation is derived. With the help of the obtained integral equations, it is shown that the potential is uniquely recovered by the given scattering data.