Nonlinear Phenomena in Complex Systems, 1999, Vol.2, No.3, pp.28--31

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

1999, Volume 2, Number 3, pp.28--31

Dynamics of Quantum Averages and Quantization Conditions in Semiclassical Approximation.
Margarita Kondrat'eva

A system of ODE which describes dynamics of quantum averages of position and momentum operators and second moments in semiclassical approximation is considered (average values are calculated w.r.t. approximate solutions of the evolution Schrödinger equation). It is shown that quantization condition for the Schrödinger operator is related to periodic solutions of the system of ODE. Known semiclassical quantization condition follows from the one obtained here under additional assumptions.

Full text: Acrobat PDF (133KB) PostScript (277KB) PostScript.gz (136KB)