Levinson's theorem as an index pairing

We build on work of Kellendonk, Richard, Tiedra de Aldecoa and others to show that the wave operators for Schrödinger scattering theory on Rn generically have a particular form. As a consequence, Levinson's theorem can be interpreted as the pairing of the K-theory class of the unitary scattering operator and the K-homology class of the generator of the group of dilations.