On negative eigenvalues of 1D Schrödinger operators with δ′-like potentials
In this paper, we investigate negative eigenvalues of exactly solvable quantum models, particularly one-dimensional Hamiltonians with δ′-like potentials used to represent localized dipoles. These operators arise as norm resolvent limits of Schrödinger operators with suitably regularized potentials....
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2025-07-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fams.2025.1615447/full |
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| _version_ | 1850117556462944256 |
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| author | Yuriy Golovaty Rostyslav Hryniv Rostyslav Hryniv |
| author_facet | Yuriy Golovaty Rostyslav Hryniv Rostyslav Hryniv |
| author_sort | Yuriy Golovaty |
| collection | DOAJ |
| description | In this paper, we investigate negative eigenvalues of exactly solvable quantum models, particularly one-dimensional Hamiltonians with δ′-like potentials used to represent localized dipoles. These operators arise as norm resolvent limits of Schrödinger operators with suitably regularized potentials. Although the limiting operator is bounded below, we show that the approximating operators may possess a finite but arbitrarily large number of negative eigenvalues that diverge to −∞ as the regularization parameter vanishes. This phenomenon illustrates a spectral instability of Schrödinger operators with δ′-like singularities. |
| format | Article |
| id | doaj-art-2e69a5d521da48b1938bdfa8ee107372 |
| institution | OA Journals |
| issn | 2297-4687 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj-art-2e69a5d521da48b1938bdfa8ee1073722025-08-20T02:36:04ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872025-07-011110.3389/fams.2025.16154471615447On negative eigenvalues of 1D Schrödinger operators with δ′-like potentialsYuriy Golovaty0Rostyslav Hryniv1Rostyslav Hryniv2Faculty of Mathematics and Mechanics, Ivan Franko National University of Lviv, Lviv, UkraineFaculty of Applied Sciences, Ukrainian Catholic University, Lviv, UkraineFaculty of Exact and Technical Sciences, University of Rzeszów, Rzeszów, PolandIn this paper, we investigate negative eigenvalues of exactly solvable quantum models, particularly one-dimensional Hamiltonians with δ′-like potentials used to represent localized dipoles. These operators arise as norm resolvent limits of Schrödinger operators with suitably regularized potentials. Although the limiting operator is bounded below, we show that the approximating operators may possess a finite but arbitrarily large number of negative eigenvalues that diverge to −∞ as the regularization parameter vanishes. This phenomenon illustrates a spectral instability of Schrödinger operators with δ′-like singularities.https://www.frontiersin.org/articles/10.3389/fams.2025.1615447/full1D Schrödinger operatorpoint interactionδ-potentialδ′-potentialexactly solvable modeldiscrete spectrum |
| spellingShingle | Yuriy Golovaty Rostyslav Hryniv Rostyslav Hryniv On negative eigenvalues of 1D Schrödinger operators with δ′-like potentials Frontiers in Applied Mathematics and Statistics 1D Schrödinger operator point interaction δ-potential δ′-potential exactly solvable model discrete spectrum |
| title | On negative eigenvalues of 1D Schrödinger operators with δ′-like potentials |
| title_full | On negative eigenvalues of 1D Schrödinger operators with δ′-like potentials |
| title_fullStr | On negative eigenvalues of 1D Schrödinger operators with δ′-like potentials |
| title_full_unstemmed | On negative eigenvalues of 1D Schrödinger operators with δ′-like potentials |
| title_short | On negative eigenvalues of 1D Schrödinger operators with δ′-like potentials |
| title_sort | on negative eigenvalues of 1d schrodinger operators with δ like potentials |
| topic | 1D Schrödinger operator point interaction δ-potential δ′-potential exactly solvable model discrete spectrum |
| url | https://www.frontiersin.org/articles/10.3389/fams.2025.1615447/full |
| work_keys_str_mv | AT yuriygolovaty onnegativeeigenvaluesof1dschrodingeroperatorswithdlikepotentials AT rostyslavhryniv onnegativeeigenvaluesof1dschrodingeroperatorswithdlikepotentials AT rostyslavhryniv onnegativeeigenvaluesof1dschrodingeroperatorswithdlikepotentials |