On the spectral gap of higher-dimensional Schrödinger operators on large domains

Article type: Research Article

Authors: Kerner, Joachim^{; **; *} | Täufer, Matthias

Affiliations: Lehrgebiet Analysis, Fakultät Mathematik und Informatik, FernUniversität in Hagen, D-58084 Hagen, Germany

Correspondence: [*] Corresponding author. E-mails: joachim.kerner@fernuni-hagen.de, kerner@uni-wuppertal.de.

Note: [**] Current address: Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppetal, 42119 Wuppertal, Germany.

Abstract: We study the asymptotic behaviour of the spectral gap of Schrödinger operators in two and higher dimensions and in a limit where the volume of the domain tends to infinity. Depending on properties of the underlying potential, we will find different asymptotic behaviours of the gap. In some cases the gap behaves as the gap of the free Dirichlet Laplacian and in some cases it does not.

Keywords: Bessel functions, fundamental gap, spectral theory, spectral gap, Schrödinger operator

DOI: 10.3233/ASY-221806

Journal: Asymptotic Analysis, vol. 133, no. 1-2, pp. 77-89, 2023