Some Spectral Properties of Schrödinger Operators on Semi Axis
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 tw...
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| Language: | English |
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Sakarya University
2023-06-01
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| Series: | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
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| Online Access: | https://dergipark.org.tr/tr/download/article-file/2907946 |
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| _version_ | 1846111370607591424 |
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| author | İbrahim Erdal |
| author_facet | İbrahim Erdal |
| author_sort | İbrahim Erdal |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-54a05bcc18e647dbae4c6ac0b2f310d5 |
| institution | Kabale University |
| issn | 2147-835X |
| language | English |
| publishDate | 2023-06-01 |
| publisher | Sakarya University |
| record_format | Article |
| series | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
| spelling | doaj-art-54a05bcc18e647dbae4c6ac0b2f310d52024-12-23T08:15:28ZengSakarya UniversitySakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi2147-835X2023-06-0127354254910.16984/saufenbilder.124011528Some Spectral Properties of Schrödinger Operators on Semi Axisİbrahim Erdal0https://orcid.org/0000-0002-4445-2389Ankara UniversityThe 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.https://dergipark.org.tr/tr/download/article-file/2907946schrödinger operatorseigenvaluesspectral singularitiesresolvent operator |
| spellingShingle | İbrahim Erdal Some Spectral Properties of Schrödinger Operators on Semi Axis Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi schrödinger operators eigenvalues spectral singularities resolvent operator |
| title | Some Spectral Properties of Schrödinger Operators on Semi Axis |
| title_full | Some Spectral Properties of Schrödinger Operators on Semi Axis |
| title_fullStr | Some Spectral Properties of Schrödinger Operators on Semi Axis |
| title_full_unstemmed | Some Spectral Properties of Schrödinger Operators on Semi Axis |
| title_short | Some Spectral Properties of Schrödinger Operators on Semi Axis |
| title_sort | some spectral properties of schrodinger operators on semi axis |
| topic | schrödinger operators eigenvalues spectral singularities resolvent operator |
| url | https://dergipark.org.tr/tr/download/article-file/2907946 |
| work_keys_str_mv | AT ibrahimerdal somespectralpropertiesofschrodingeroperatorsonsemiaxis |