Geodesic
On the Delocalization of a Quantum Particle under the Adiabatic Evolution Generated by a One-Dimensional Schr\"odinger Operator
Matematičeskie zametki, Tome 112 (2022) no. 5, pp. 752-769

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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 $\sigma_c=[0,+\infty)$ and finitely many negative eigenvalues. In time, the eigenvalues approach the edge of $\sigma_c$ 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 $\lambda$ exists, the solution is localized inside the potential well. Its delocalization with the disappearance of $\lambda$ is described.
Keywords: one-dimensional nonstationary Schrödinger operator, delocalization of a quantum state
Mots-clés : adiabatic evolution. 
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     author = {V. A. Sergeev and A. A. Fedotov},
     title = {On the {Delocalization} of a {Quantum} {Particle} under the {Adiabatic} {Evolution} {Generated} by a {One-Dimensional} {Schr\"odinger} {Operator}},
     journal = {Matemati\v{c}eskie zametki},
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V. A. Sergeev; A. A. Fedotov. On the Delocalization of a Quantum Particle under the Adiabatic Evolution Generated by a One-Dimensional Schr\"odinger Operator. Matematičeskie zametki, Tome 112 (2022) no. 5, pp. 752-769. http://geodesic.mathdoc.fr/item/MZM_2022_112_5_a8/