Unstable quantum states and rigged Hilbert spaces

  • V. Gorini
  • G. Parravicini
Groups and Semigroups in the Description of Decaying Systems
Part of the Lecture Notes in Physics book series (LNP, volume 94)


We apply rigged Hilbert space techniques to the quantum mechanical treatment of unstable states in nonrelativistic scattering theory.We discuss a method which is based on representations of decay amplitudes in terms of expansions over complete sets of generalized eigenvectors of the interacting Hamiltonian, corresponding to complex eigenvalues.These expansions contain both a “discrete” and a “continuum” contribution. The former corresponds to eigenvalues located at the second sheet poles of the S matrix, and yields the exponential terms in the survival amplitude. The latter arises from generalized eigenvectors associated to complex eigenvalues on background contours in the complex plane, and gives the corrections to the exponential law.


Analytic Continuation Unstable State Complex Eigenvalue Analytic Family Laurent Expansion 
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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • V. Gorini
    • 1
    • 2
  • G. Parravicini
    • 1
  1. 1.Physics Department, CPTThe University of Texas at AustinAustin
  2. 2.Istituto di Fisica dell 'UniversitáMilanoItaly

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