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 R n 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. [ABSTRACT FROM AUTHOR]