Preprint

Inserted: 30 sep 2024
Last Updated: 30 sep 2024

Pages: 35
Year: 2024

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.pdf