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Matematicheskie Zametki, 2024, Volume 116, Issue 4, paper published in the English version journal (Mi mzm14524)  

Papers published in the English version of the journal

Adiabatic evolution generated by a one-dimensional Schrödinger operator with decreasing number of eigenvalues

A. A. Fedotov

Saint Petersburg State University
Abstract: We study a one-dimensional nonstationary Schrödinger equation with a potential slowly depending on time. The corresponding stationary operator depends on time as on a parameter. It has finitely many negative eigenvalues and absolutely continuous spectrum filling $[0,+\infty)$. The eigenvalues move with time to the edge of the continuous spectrum and, having reached it, disappear one after another. We describe the asymptotic behavior of a solution close at some moment to an eigenfunction of the stationary operator, and, in particular, the phenomena occurring when the corresponding eigenvalue approaches the absolutely continuous spectrum and disappears.
Keywords: adiabatic evolution, stationary, generating solution, saddle point.
Funding agency Grant number
Russian Science Foundation 22-11-00092
This work was financially supported by the Russian Science Foundation, project 22-11-00092, https://rscf.ru/en/project/22-11-00092/.
Received: 12.09.2024
Revised: 12.09.2024
English version:
Mathematical Notes, 2024, Volume 116, Issue 4, Pages 804–830
DOI: https://doi.org/10.1134/S0001434624090360
Bibliographic databases:
Document Type: Article
Language: English
Citation: A. A. Fedotov, “Adiabatic evolution generated by a one-dimensional Schrödinger operator with decreasing number of eigenvalues”, Math. Notes, 116:4 (2024), 804–830
Citation in format AMSBIB
\Bibitem{Fed24}
\by A.~A.~Fedotov
\paper Adiabatic evolution generated by a one-dimensional Schr\"odinger operator with decreasing number of eigenvalues
\jour Math. Notes
\yr 2024
\vol 116
\issue 4
\pages 804--830
\mathnet{http://mi.mathnet.ru/mzm14524}
\crossref{https://doi.org/10.1134/S0001434624090360}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85213481513}
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