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)

Abstract

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:
$$ \begin{gathered} \left\langle {\dot x} \right\rangle = \left\langle p \right\rangle /m, \hfill \\ \left\langle {\dot p} \right\rangle = - \left\langle {V\left( x \right)} \right\rangle . \hfill \\\end{gathered} $$

Keywords

Normal Form Power Transformation Quantum Particle Resonance Relation Casimir Function 
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References

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    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

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