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Scattering States

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

Abstract

In this chapter we study scattering states in a little more det ail. As we saw in Section 5.4, scattering states are solutions of the time-dependent Schrödinger equation
$$ i\hbar \frac{{\partial \psi }} {{\partial t}} = H\psi $$
(6.1)
with initial condit ion orthogonal to all eigenfunctions of H:
$$ \psi |_{t = 0} = \psi _0 \in \mathcal{H}\frac{1} {b} $$
(6.2)
where H b := span eigenfunctions of H is the subspace of bound states of H.

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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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