These are the written notes of Fermi's Lectures supported by the Accademia Nazionale dei Lincei and given at the Scuola Normale Superiore of Pisa during March-April 1973. We propose to discuss here certain spectral properties of Schrödinger operators H=-D+V(x) (D the Laplacian and V a potential) which have application to scattering theory. We consider an operator H with potential V of class SR. We show that the positive point spectrum of H is a discrete set in R+. Eigenfunctions which correspond to positive eigenvalues are shown to decay rapidly. This property is shown to hold also for generalized eigenfunctions. We then establish the limiting absorbing principle, which is a basic tool in our study.
- ISBN13 9788876422478
- Publish Date 1 October 1975
- Publish Status Active
- Publish Country IT
- Publisher Birkhauser Verlag AG
- Imprint Scuola Normale Superiore
- Edition 1975 ed.
- Format Paperback
- Pages 68
- Language English