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<p>We use spectral flow to present a new proof of Levinson’s theorem for Schrödinger operators on <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43034_2025_418_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {R}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation> with smooth compactly supported potential. Our proof is valid in all dimensions and in the presence of resonances. The statement is expressed in terms of the spectral shift function and the “high energy corrected time delay” following Guillopé and others.</p>

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Spectral flow and Levinson’s theorem for Schrödinger operators

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月28日

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  • Angus Alexander,
  • Adam Rennie

摘要

We use spectral flow to present a new proof of Levinson’s theorem for Schrödinger operators on \(\mathbb {R}^n\) R n with smooth compactly supported potential. Our proof is valid in all dimensions and in the presence of resonances. The statement is expressed in terms of the spectral shift function and the “high energy corrected time delay” following Guillopé and others.