Mat. Zametki, 2012 Volume 92, Issue 2, Pages 163–180
(Mi mzm9749)
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14 papers
Averaging of Linear Operators, Adiabatic Approximation, and Pseudodifferential Operators J. Brüning a ,
V. V. Grushin bc ,
S. Yu. Dobrokhotov dc a Humboldt University, Germany b Moscow State Institute of Electronics and Mathematics c Moscow Institute of Physics and Technology d A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences Abstract:
An example of Schrödinger and Klein–Gordon equations with fast oscillating coefficients is used to show that they can be averaged by an adiabatic approximation based on V. P. Maslov's operator method.
Keywords:
Klein–Gordon equation, Schrödinger equation, adiabatic approximation, asymptotic solution, pseudodifferential operator, adiabatic principle, perturbation theory.
UDC:
517.9
Received: 28.12.2011
DOI:
10.4213/mzm9749
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