Accepted Paper

Inserted: 30 sep 2024
Last Updated: 25 apr 2025

Journal: Anal. Math. Phys.
Pages: 36
Year: 2025

Abstract:

We study the spectral properties of a Sch\"rodinger operator, in presence of a confining potential given by the distance squared from a fixed compact potential well. We prove continuity estimates on both the eigenvalues and the eigenstates, lower bounds on the ground state energy, regularity and integrability properties of eigenstates. We also get explicit decay estimates at infinity, by means of elementary nonlinear methods.

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• confinedschroedinger_final_rev.pdf