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Spectral Theory

  • Stephen J. Gustafson
  • Israel Michael Sigal
Part of the Universitext book series (UTX)

Abstract

Our next task is to classify the orbits (i.e. solutions) of the Schrödinger equation
$$ i\hbar \frac{{\partial \psi }} {{\partial t}} = H\psi $$
with given initial condition
$$ \psi |_{t = 0} = \psi _0 $$
according to their behaviour in space-time. Naturally, we want to distinguish between states which are localized for all time, and those whose essential support moves off to infinity. Such a classification is made with the help of a very important notion — the spectrum of an operator. We begin by describing the general theory, and then we proceed to applications.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Stephen J. Gustafson
    • 1
  • Israel Michael Sigal
    • 2
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada

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