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


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


Bounded Operator Symmetric Operator Schrodinger Equation Free Propagator Plancherel Theorem 
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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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