Geodesic
Averaging of Linear Operators, Adiabatic Approximation, and Pseudodifferential Operators
Matematičeskie zametki, Tome 92 (2012) no. 2, pp. 163-180

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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.
Mots-clés : Klein–Gordon equation
Keywords: Schrödinger equation, adiabatic approximation, asymptotic solution, pseudodifferential operator, adiabatic principle, perturbation theory. 
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     author = {J. Br\"uning and V. V. Grushin and S. Yu. Dobrokhotov},
     title = {Averaging of {Linear} {Operators,} {Adiabatic} {Approximation,} and {Pseudodifferential} {Operators}},
     journal = {Matemati\v{c}eskie zametki},
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     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_2_a0/}
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J. Brüning; V. V. Grushin; S. Yu. Dobrokhotov. Averaging of Linear Operators, Adiabatic Approximation, and Pseudodifferential Operators. Matematičeskie zametki, Tome 92 (2012) no. 2, pp. 163-180. http://geodesic.mathdoc.fr/item/MZM_2012_92_2_a0/