Problems Connected with Discrete Spectra

  • K. Chadan
  • P. C. Sabatier
  • R. G. Newton
Part of the Texts and Monographs in Physics book series (TMP)

Abstract

When a vibration is created in a finite structure, its energy may be divided into a set of well-defined vibrations that are called modes of the system. The mathematical model is usually the spectral problem of a linear operator. The modes are then associated with eigenvalues and eigenfunctions (e.g., vibrating strings, etc.). A “continuous extension” of these problems is observed in scattering studies (see chapter II). There are linear operators showing a discrete spectrum, a continuous spectrum, and an exceptional spectrum; and there are also nonlinear systems exhibiting a generalized discrete spectrum. However, we shall stay with the “generic” (most simple) cases and their relations to quantum inverse scattering.

Keywords

Sine Verse 

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Copyright information

© Springer-Verlag New York Inc. 1989

Authors and Affiliations

  • K. Chadan
    • 1
  • P. C. Sabatier
    • 2
  • R. G. Newton
    • 3
  1. 1.Laboratoire de Physique ThéoriqueUniversité de Paris-SudOrsayFrance
  2. 2.Université des Sciences et Techniques du LanguedocMontpellier CedexFrance
  3. 3.Department of PhysicsIndiana UniversityBloomingtonUSA

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