Year: 2025
Type: article
Abstract: In the present paper, motivated by point interaction, we propose a new and explicit approach to inverse Sturm-Liouville eigenvalue problems under Dirichlet boundary. More precisely, when a given Sturm-Liouville eigenvalue problem with the unknown integrable potential interacts with δ-function potentials, we obtain a family of perturbation problems, called point interaction models in quantum mechanics. Then, only depending on the first eigenvalues of these perturbed problems, we define and study the first eigenvalue function, by which the desired potential can be expressed explicitly and uniquely. As by-products, using the analytic function theoretic tools, we also generalize several fundamental theorems of classical Sturm-Liouville problems to measure differential equations with non-trivial positive integrable weights, which provide the possibility of the further study of inverse spectral problems for more general measure differential equations.
Source: Journal of Mathematical Physics
DOI: 10.1063/5.0230925
Authors: Min Zhao, Jiangang Qi, Xiao Chen
Institution: Shandong University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1203995475, G2374269290, G5826441121
OpenAlex ID: W4408615309