ORIGINAL RESEARCH article
Front. Appl. Math. Stat.
Sec. Mathematical Physics
Volume 11 - 2025 | doi: 10.3389/fams.2025.1615447
This article is part of the Research TopicRecent Mathematical and Theoretical Progress in Quantum MechanicsView all 3 articles
ON NEGATIVE EIGENVALUES OF 1D SCHRÖDINGER OPERATORS WITH δ ′ -LIKE POTENTIALS
Provisionally accepted
- 1Ivan Franko National University of Lviv, Lviv, Ukraine
- 2Ukrainian Catholic University, Lviv, Ukraine
- 3University of Rzeszow, Rzeszów, Podkarpackie Voivodeship, Poland
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We study the asymptotic behavior of the discrete spectrum of onedimensional Schrödinger operators with δ ′ -like potentials, which are used to construct exactly solvable models for localized dipoles in quantum mechanics. Although these operators converge in the norm resolvent topology to a limiting operator that is bounded from below, we prove that they can possess a finite but arbitrarily large number of discrete eigenvalues that diverge to negative infinity as the regularization parameter tends to zero. This phenomenon illustrates a spectral instability of Schrödinger operators with these singular potentials.
Keywords: 2020 Mathematics Subject Classification. Primary 81Q10; Secondary 34L40 1D Schrödinger operator, point interaction, δ-potential, δ ′ -potential, solvable model, Discrete spectrum
Received: 21 Apr 2025; Accepted: 17 Jun 2025.
Copyright: © 2025 Golovaty and Hryniv. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Yuriy Golovaty, Ivan Franko National University of Lviv, Lviv, Ukraine
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