Time-Dependent Perturbation Theory

  • Alberto Galindo
  • Pedro Pascual
Part of the Texts and Monographs in Physics book series (TMP)


In previous chapters we have learned how to solve either exactly or approximately the time-independent Schrödinger equation. This is however not enough in general, for there are many instances where one is required to understand the time evolution of a quantum system. If the Hamiltonian in the Schrödinger picture is H(t), the equation we want to integrate is
$$ i\hbar \frac{{d\left| {\Psi (t)} \right\rangle }}{{dt}} = H(t)\left| {\Psi (t)} \right\rangle $$
assuming |Ψ(t0)〉 is known. This is equivalent to the computation of the operator U(t, t0) introduced in Chap. 2. In most cases the mathematical structure of H(t) is so complicated that no practical methods of computation are available.


Evolution Operator Born Approximation Adiabatic Approximation Interaction Picture Adiabatic Theorem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Alberto Galindo
    • 1
  • Pedro Pascual
    • 2
  1. 1.Facultad de Ciencias Físicas, Departamento de Física TeóricaUniversidad ComplutenseMadridSpain
  2. 2.Facultad de Física, Departamento de Física TeóricaUniversidad de BarcelonaBarcelonaSpain

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