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This article is cited in 2 scientific papers (total in 2 papers)
On the Delocalization of a Quantum Particle under the Adiabatic Evolution Generated by a One-Dimensional Schrödinger Operator
V. A. Sergeevab, A. A. Fedotova a Saint Petersburg State University
b Euler International Mathematical Institute, St. Petersburg
Abstract:
The one-dimensional nonstationary Schrödinger equation is discussed in the adiabatic approximation. The corresponding stationary operator H, 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.
Received: 07.06.2022 Revised: 26.06.2022
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
Linking options:
https://www.mathnet.ru/eng/mzm13776https://doi.org/10.4213/mzm13776 https://www.mathnet.ru/eng/mzm/v112/i5/p752
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Abstract page: | 275 | Full-text PDF : | 53 | References: | 76 | First page: | 9 |
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