Trace formula and Levinson’s theorem as an index pairing in the presence of resonances.

We realize the number of bound states of a Schrödinger operator on ℝn as an index pairing in all dimensions. Expanding on ideas of Guillopé and others, we use high-energy corrections to find representatives of the K-theory class of the scattering operator. These representatives allow us to compute the number of bound states using an integral formula involving heat kernel coefficients. [ABSTRACT FROM AUTHOR]