ON THE SEMI-CLASSICAL ANALYSIS OF SCHRÖDINGER OPERATORS WITH LINEAR ELECTRIC POTENTIALS ON A BOUNDED DOMAIN - Laboratoire Angevin de Recherche en Mathématiques Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

ON THE SEMI-CLASSICAL ANALYSIS OF SCHRÖDINGER OPERATORS WITH LINEAR ELECTRIC POTENTIALS ON A BOUNDED DOMAIN

Résumé

The aim of this paper is to establish the asymptotic expansion of the eigenvalues of the Stark Hamiltonian, with strong uniform electric field and Dirichlet boundary conditions on a smooth bounded domain of R N , N ≥ 2. This work aims at generalizing the recent results of Cornean, Krejcirik, Pedersen, Raymond and Stockmeyer in dimension 2. More precisely, in dimension N , in the strong electric field limit, we derive, under certain local convexity conditions, a full asymptotic expansion of the low-lying eigenvalues. To establish our main result, we perform the construction of quasi-modes. The "optimality" of our constructions is then established thanks to a reduction to model operators and localization estimates. In addition, we apply our techniques to find a full asymptotic expansion of the low-lying eigenvalues of more general operator −h 2 ∆+V (x) where h is a small parameter and V is a smooth real potential satisfies some additional conditions.
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Dates et versions

hal-03875344 , version 1 (28-11-2022)
hal-03875344 , version 2 (16-03-2023)

Identifiants

  • HAL Id : hal-03875344 , version 1

Citer

Rayan Fahs. ON THE SEMI-CLASSICAL ANALYSIS OF SCHRÖDINGER OPERATORS WITH LINEAR ELECTRIC POTENTIALS ON A BOUNDED DOMAIN. 2022. ⟨hal-03875344v1⟩
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