On the spectral gap of higher-dimensional Schrödinger operators on large domains
Joachim Kerner, Matthias Täufer · Asymptotic Analysis · 2022
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.