Geodesic
Adiabatic Evolution Generated by a Schr\"odinger Operator with Discrete and Continuous Spectra
Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 1, pp. 90-93

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In the paper, we consider the one-dimensional nonstationary Schrödinger equation with a potential slowly depending on time. It is assumed that the corresponding stationary operator depending on time as a parameter has a finite number of negative eigenvalues and absolutely continuous spectrum filling the positive semiaxis. A solution close at some moment to an eigenfunction of the stationary operator is studied. We describe its asymptotic behavior in the case where the eigenvalues of the stationary operator move to the edge of the continuous spectrum and, having reached it, disappear one after another.
Keywords: Schrödinger operator, absolutely continuous spectrum, discrete spectrum.
Mots-clés : adiabatic evolution 
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     title = {Adiabatic {Evolution} {Generated} by a {Schr\"odinger} {Operator} with {Discrete} and {Continuous} {Spectra}},
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A. B. Smirnov; A. A. Fedotov. Adiabatic Evolution Generated by a Schr\"odinger Operator with Discrete and Continuous Spectra. Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 1, pp. 90-93. http://geodesic.mathdoc.fr/item/FAA_2016_50_1_a9/