Eigenvalues asymptotics for Stark operators
Authors: Hatem Najar, Monia Raissi
Journal: e-Journal of Analysis and Applied Mathematics (e-JAAM), e-ISSN 2544-9990
Volume: 2019 · Pages: 1 - 14
Published Online: 25 Jul 2019
Abstract: We give the eigenvalues asymptotics for the Stark operator of the form -Δ+Fx, F>0 on 2([0,d]). This is given in the case when F is small enough or sufficiently large. We impose various boundary conditions. The proof is based on the asymptotics of the specialized Airy functions.
Keywords: Spectral theory, Schrödinger operator, Dirichlet and Neumann Laplacian, Stark operator, Eigenvalue problem, Airy functions