We consider a model of one-dimensional Schr\"odinger Hamiltonian perturbed by two identical non-local interactions of the form $\delta'(x\pm y)$, symmetrically located at the points $ \pm y$ from the origin. The Schr\"odinger operator under consideration is constructed as a self-adjoint extension of the symmetric Laplacian. The essential spectrum is described, and the condition for the existence of the eigenvalue of the Schr\"odinger operator is investigated. The main results are based on the analysis of the spectral analysis of self-adjoint extension of the operator $\mathbf{h}$.
| Mualliflar | Ismoilov, G. |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashriyot | Ўзбекистон Республикаси ФА Математика институти |
| ISSN | 2010-7269 |
| Nashr sanasi | 2026-03-25 |
| Jild | 70 |
| Son | 1 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.29229/uzmj.2026-1-10 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2026-1-10 · Maqolaning asl sahifasi
Schr\"{o}dinger operators, non-local delta prime interactions, eigenvalues, eigenfunctions
| APA | Ismoilov, G. (2026). Spectral properties of the one-dimensional Schrödinger Hamiltonian with non-local $\delta'(x\pm y)$ potentials. O‘zbekiston matematika jurnali, 70(1). https://doi.org/10.29229/uzmj.2026-1-10 |
|---|---|
| GOST (OAK) | Ismoilov, G. Spectral properties of the one-dimensional Schrödinger Hamiltonian with non-local $\delta'(x\pm y)$ potentials // O‘zbekiston matematika jurnali. – 2026. – T. 70, № 1. – DOI: 10.29229/uzmj.2026-1-10. |
| MLA | Ismoilov, G. “Spectral properties of the one-dimensional Schrödinger Hamiltonian with non-local $\delta'(x\pm y)$ potentials.” O‘zbekiston matematika jurnali, 70(1), 2026. https://doi.org/10.29229/uzmj.2026-1-10 |
| Chicago | Ismoilov, G. “Spectral properties of the one-dimensional Schrödinger Hamiltonian with non-local $\delta'(x\pm y)$ potentials.” O‘zbekiston matematika jurnali, 70(1) (2026). https://doi.org/10.29229/uzmj.2026-1-10 |
| Harvard | Ismoilov, G (2026) ‘Spectral properties of the one-dimensional Schrödinger Hamiltonian with non-local $\delta'(x\pm y)$ potentials’, O‘zbekiston matematika jurnali, 70(1). https://doi.org/10.29229/uzmj.2026-1-10 |
| BibTeX | @article{ismoilovg2026,
title = {Spectral properties of the one-dimensional Schrödinger Hamiltonian with non-local $\delta'(x\pm y)$ potentials},
author = {Ismoilov, G.},
journal = {O‘zbekiston matematika jurnali},
year = {2026},
volume = {70},
number = {1},
doi = {10.29229/uzmj.2026-1-10},
url = {https://doi.org/10.29229/uzmj.2026-1-10}
} |
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