Abstract:
The one-dimensional nonstationary Schrödinger equation is discussed in the adiabatic approximation. The corresponding stationary operator HH, depending on time as a parameter, has a continuous spectrum σc=[0,+∞) and finitely many negative eigenvalues. In time, the eigenvalues approach the edge of σc and disappear one by one. The solution under consideration is close at some moment to an eigenfunction of H. As long as the corresponding eigenvalue λ exists, the solution is localized inside the potential well. Its delocalization with the disappearance of λ is described.
Keywords:
one-dimensional nonstationary Schrödinger operator, delocalization of a quantum state, adiabatic evolution.
Citation:
V. A. Sergeev, A. A. Fedotov, “On the Delocalization of a Quantum Particle under the Adiabatic Evolution Generated by a One-Dimensional Schrödinger Operator”, Mat. Zametki, 112:5 (2022), 752–769; Math. Notes, 112:5 (2022), 726–740
\Bibitem{SerFed22}
\by V.~A.~Sergeev, A.~A.~Fedotov
\paper On the Delocalization of a Quantum Particle under the Adiabatic Evolution Generated by a One-Dimensional Schr\"odinger Operator
\jour Mat. Zametki
\yr 2022
\vol 112
\issue 5
\pages 752--769
\mathnet{http://mi.mathnet.ru/mzm13776}
\crossref{https://doi.org/10.4213/mzm13776}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4538803}
\transl
\jour Math. Notes
\yr 2022
\vol 112
\issue 5
\pages 726--740
\crossref{https://doi.org/10.1134/S0001434622110098}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85145899334}
Linking options:
https://www.mathnet.ru/eng/mzm13776
https://doi.org/10.4213/mzm13776
https://www.mathnet.ru/eng/mzm/v112/i5/p752
This publication is cited in the following 2 articles:
V. A. Sergeev, A. A. Fedotov, “O poverkhnostnoi volne, voznikayuschei posle delokalizatsii kvantovoi chastitsy pri adiabaticheskoi evolyutsii”, Algebra i analiz, 36:1 (2024), 204–233
V.A. Sergeev, “On the Upslope Propagation of an Adiabatic Normal Mode in a Wedge-Shaped Sea”, Russ. J. Math. Phys., 31:2 (2024), 308