Advertisement

Dynamics

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

Abstract

We recall that the evolution of the wave function, ψ, for a particle in a potential, V, is determined by the Schrödinger equation:
$$ i\hbar \frac{{\partial \psi }} {{\partial t}} = H\psi $$
(2.1)
where
$$ H = - \frac{{\hbar ^2 }} {{2m}}\Delta + V $$
is the appropriate Schrödinger operator. We supplement equation (2.1) with the initial condition
$$ \psi |_{t = 0} = \psi _0 $$
(2.2)
where ψ0L2. The problem of solving (2.1)– (2.2) is called an initial value problem or a Cauchy problem.

Keywords

Bounded Operator Symmetric Operator Schrodinger Equation Free Propagator Plancherel Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations