A Study of a Finite-Dimensional Dynamical System Approximating the Evolution of Quantum Averages

  • S. Yu. Sadov
Part of the NATO ASI Series book series (NSSB, volume 331)


Among the earliest results of quantum mechanics there is P. Ehrenfest’s theorem which states that the averages of coordinate and momentum of a quantum particle in the potential V(x) vary as follows:
$$ \begin{gathered} \left\langle {\dot x} \right\rangle = \left\langle p \right\rangle /m, \hfill \\ \left\langle {\dot p} \right\rangle = - \left\langle {V\left( x \right)} \right\rangle . \hfill \\\end{gathered} $$


Normal Form Power Transformation Quantum Particle Resonance Relation Casimir Function 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bel).
    V.V. Belov, Quasi-classical trajectory-coherent approximation in the quantum theory, Thesis (D.Sc), Moscow, 1991, p.130.Google Scholar
  2. BBK).
    V.G. Bagrov, V.V. Belov, M.F. Kondrat’eva, Quasi-classical approximation in quantum mechanics. A new approach, being printed in: Theor.& math. phys.Google Scholar
  3. Br1).
    A.D. Bruno, Local methods in nonlinear differential equations, Springer-Verlag, Berlin, 1989.CrossRefzbMATHGoogle Scholar
  4. Br2).
    A.D. Bruno, Bifurcation of the periodic solutions in the symmetric case of a multiple pair of imaginary eigenvalues, Selecta Mathematica, v. 12, 1, 1993.MathSciNetADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • S. Yu. Sadov
    • 1
  1. 1.MoscowRussia

Personalised recommendations