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Book Synopsis
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.

Spectral properties of Schroedinger operators and

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    A Paperback / softback by Shmuel Agmon

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      Publisher: Birkhauser Verlag AG
      Publication Date: 01/10/1975
      ISBN13: 9788876422478, 978-8876422478
      ISBN10: 8876422471
      Also in:
      Mathematical / Computational / Theoretical physics

      Description

      Book Synopsis
      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.

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