Problems Connected with Discrete Spectra

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


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.


Inverse Problem Spectral Function Discrete Spectrum Spectral Problem Inverse Spectral Problem 
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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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