Spectral flow and Levinson's theorem for Schrö dinger operators

Abstract: We use spectral flow to present a new proof of Levinson's theorem for Schr\"{o}dinger operators on $\mathbb{R}^n$ 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 Guillop\'{e} and others.