Some Spectral Properties of Schrödinger Operators on Semi Axis
Yıl: 2023 Cilt: 27 Sayı: 3 Sayfa Aralığı: 542 - 549 Metin Dili: İngilizce DOI: 10.16984/saufenbilder.1240115 İndeks Tarihi: 07-07-2023
Some Spectral Properties of Schrödinger Operators on Semi Axis
Öz: The main aim of this work is to investigate some spectral properties of Schrödinger operators on semi axis. We first present the Schrödinger equation with a piecewise continuous potential function q so that the problem differs from the classical Schrödinger problems. Then, we get the Wronskian of two specific solution of the given equation which helps us to create the sets of eigenvalues and spectral singularities. The rest of the paper deals with eigenvalues and spectral singularities. By the help of the analytical properties of Jost solutions and resolvent operator of the Schrödinger operators, we provide sufficient conditions guarenteeing finiteness of eigenvalues and spectral singularities with finite multiplicities.
Anahtar Kelime: Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
- [1] M. A. Naimark, “Investigation of the spectrum and the expansion in eigenfunctions of a non-selfadjoint operators of second order on a semi-axis,” American Mathematical Society Translations: Series 2. vol. 2, no.16, pp. 103-193, 1960.
- [2] J. T. Schwartz, “Some non-selfadjoint operators,” Communications on Pure and Applied Mathematics, vol. 13, pp. 609-639, 1960.
- [3] V. A. Marchenko, “Sturm-Liouville Operators and Applications Operator Theory: Advances and Applications,” vol. 22, Birkhauser, Basel 1986.
- [4] B. M. Levitan, I. S. Sargsjan, “Sturm-Liouville and Dirac Operators,” Kluwer Academic Publishers, 1991.
- [5] E. Bairamov, A. O. Celebi, “Spectral analysis of nonselfadjoint Schrödinger operators with spectral parameter in boundary conditions,” Facta Universitatis, Series: Mathematics and Informatics, vol. 13, pp. 79-94, 1998.
- [6] E. Bairamov, O. Cakar, A. M. Krall, “An eigenfunction expansion for a quadratic pencil of a Schrödinger operator with spectral singularities,” Journal of Differential Equations, vol. 151, pp. 268-289, 1999.
- [7] M. Adıvar, E. Bairamov, “ Spectral singularities of the nonhomogeneous Sturm-Liouville equations,” Applied Mathematics Letters, vol. 15, no.7, pp. 825-832, 2002.
- [8] E. Bairamov, E. Kir, ”Spectral properties of a finite system of Sturm-Liouville differential operators,” Indian Journal of Pure and Applied Mathematics, vol. 35, no.2, pp. 249-256, 2004.
- [9] G. Sh. Guseinov, “On the concept of spectral singularities,” Pramana-Journal of Physics, vol. 73, no.3, pp. 587-603, 2009.
- [10] A. M. Krall, E. Bairamov, O. Cakar, “Spectrum and spectral singularities of a quadratic pencil of a Schrödinger operator with a general boundary condition,” Journal of Differential Equations, vol. 151, no.2, pp. 252-267, 1999.
- [11] A. Mostafazadeh, “Optical spectral singularities as treshold resonances,” Physical Review A Third Series-83:045801, 2011.
- [12] E. Bairamov, S. Cebesoy, “Spectral singularities of the matrix Schrödinger equations,” Hacettepe Journal of Mathematics and Statistics, vol. 45, no.4, pp. 1007-1014, 2016.
- [13] S. Cebesoy, “Examination of eigenvalues and spectral singularities of a discrete Dirac operator with an interaction point,” Turkish Journal of Mathematics, vol. 46, no.1, pp. 157-166, 2022.
- [14] Ş. Yardımcı, İ. Erdal, “Investigation of an impulsive Sturm-Liouville operator on semi axis,” Hacettepe Journal of Mathematics and Statistics, vol. 48, no.5, pp. 1409-1416, 2019.
- [15] Y. Aygar, G. G. Özbey, “Scattering analysis of a quantum impulsive boundary value problem with spectral parameter,” Hacettepe Journal of Mathematics and Statistics, vol. 51, no.1, pp. 142-155, 2022.
- [16] T. Köprübaşi, Y. Aygar Küçükevcilioğlu, “Discrete impulsive Sturm-Liouville equation with hyperbolic eigenparameter,” Turkish Journal of Mathematics, vol. 46, no.2, pp. 387-396, 2022.
- [17] E. P. Dolzhenko, “Boundary value uniqueness theorems for analytic functions,” Mathematical Notes, vol. 26, pp. 437-442, 1979.
- [18] B. S. Pavlov, “The non-selfadjoint Schrödinger operators,” Mathematical Physics, vol. 1, pp. 87-114, 1967.
| APA | Erdal İ (2023). Some Spectral Properties of Schrödinger Operators on Semi Axis. , 542 - 549. 10.16984/saufenbilder.1240115 |
| Chicago | Erdal İbrahim Some Spectral Properties of Schrödinger Operators on Semi Axis. (2023): 542 - 549. 10.16984/saufenbilder.1240115 |
| MLA | Erdal İbrahim Some Spectral Properties of Schrödinger Operators on Semi Axis. , 2023, ss.542 - 549. 10.16984/saufenbilder.1240115 |
| AMA | Erdal İ Some Spectral Properties of Schrödinger Operators on Semi Axis. . 2023; 542 - 549. 10.16984/saufenbilder.1240115 |
| Vancouver | Erdal İ Some Spectral Properties of Schrödinger Operators on Semi Axis. . 2023; 542 - 549. 10.16984/saufenbilder.1240115 |
| IEEE | Erdal İ "Some Spectral Properties of Schrödinger Operators on Semi Axis." , ss.542 - 549, 2023. 10.16984/saufenbilder.1240115 |
| ISNAD | Erdal, İbrahim. "Some Spectral Properties of Schrödinger Operators on Semi Axis". (2023), 542-549. https://doi.org/10.16984/saufenbilder.1240115 |
| APA | Erdal İ (2023). Some Spectral Properties of Schrödinger Operators on Semi Axis. Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 27(3), 542 - 549. 10.16984/saufenbilder.1240115 |
| Chicago | Erdal İbrahim Some Spectral Properties of Schrödinger Operators on Semi Axis. Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi 27, no.3 (2023): 542 - 549. 10.16984/saufenbilder.1240115 |
| MLA | Erdal İbrahim Some Spectral Properties of Schrödinger Operators on Semi Axis. Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol.27, no.3, 2023, ss.542 - 549. 10.16984/saufenbilder.1240115 |
| AMA | Erdal İ Some Spectral Properties of Schrödinger Operators on Semi Axis. Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi. 2023; 27(3): 542 - 549. 10.16984/saufenbilder.1240115 |
| Vancouver | Erdal İ Some Spectral Properties of Schrödinger Operators on Semi Axis. Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi. 2023; 27(3): 542 - 549. 10.16984/saufenbilder.1240115 |
| IEEE | Erdal İ "Some Spectral Properties of Schrödinger Operators on Semi Axis." Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 27, ss.542 - 549, 2023. 10.16984/saufenbilder.1240115 |
| ISNAD | Erdal, İbrahim. "Some Spectral Properties of Schrödinger Operators on Semi Axis". Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi 27/3 (2023), 542-549. https://doi.org/10.16984/saufenbilder.1240115 |
