Spectral flow and Levinson’s theorem for Schrödinger operators

Abstract We use spectral flow to present a new proof of Levinson’s theorem for Schrödinger operators on $$\mathbb {R}^n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:math> 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.