Use of Quantum Trajectories for Time-Dependent Problems

  • M. Kleber
Part of the NATO ASI Series book series (NSSB, volume 135)


Ehrenfest’s principle states the correspondence between a classical trajectory and the expectation values of the corresponding quantum operator. In most cases the equations of motion for the average values of momentum, position, etc. are not closed and, therefore, cannot be solved without further assumptions. It is then useful to rewrite the Schrodinger equation as a time-dependent eigenvalue equation. In the following we shall outlines (1) how to solve the eigenvalue problem within variational perturbation theory, (2) how to calculate quantum trajectories, and (3) how to determine transition probabilities from trajectories. The method presented here will be illustrated by two examples from scattering theory.


Wave Function Variational Principle Classical Trajectory Gaussian Wave Packet Trial Wave Function 
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Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • M. Kleber
    • 1
    • 2
  1. 1.Institute for Theoretical SciencesUniversity of New MexicoAlbuquerqueUSA
  2. 2.Physik DepartmentT. U. MünchenGarching bei MünchenWest Germany

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