On the Spectrum of the Two-Particle Schrödinger Operator with Point Potential: Two Dimensional Case
In the article, a two-dimensional two-particle quantum system interacted by two identical point interactions is studied. The corresponding Schrödinger operator (energy operator) depending on is constructed as a self-adjoint extension of the symmetric Laplace operator. The essential spectrum of is de...
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| Published in | Lobachevskii journal of mathematics Vol. 46; no. 1; pp. 456 - 463 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Moscow
Pleiades Publishing
01.01.2025
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1995-0802 1818-9962 |
| DOI | 10.1134/S1995080224608105 |
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| Abstract | In the article, a two-dimensional two-particle quantum system interacted by two identical point interactions is studied. The corresponding Schrödinger operator (energy operator)
depending on
is constructed as a self-adjoint extension of the symmetric Laplace operator. The essential spectrum of
is described. The existence of unique eigenvalue of the Schrödinger operator is proved and corresponding eigenfunction to this eigenvalue is found. |
|---|---|
| AbstractList | In the article, a two-dimensional two-particle quantum system interacted by two identical point interactions is studied. The corresponding Schrödinger operator (energy operator) depending on is constructed as a self-adjoint extension of the symmetric Laplace operator. The essential spectrum of is described. The existence of unique eigenvalue of the Schrödinger operator is proved and corresponding eigenfunction to this eigenvalue is found. In the article, a two-dimensional two-particle quantum system interacted by two identical point interactions is studied. The corresponding Schrödinger operator (energy operator) depending on is constructed as a self-adjoint extension of the symmetric Laplace operator. The essential spectrum of is described. The existence of unique eigenvalue of the Schrödinger operator is proved and corresponding eigenfunction to this eigenvalue is found. |
| Author | Kuljanov, U. N. |
| Author_xml | – sequence: 1 givenname: U. N. surname: Kuljanov fullname: Kuljanov, U. N. email: uquljonov@bk.ru organization: Sharof Rashidov Samarkand State University, Samarkand Branch of Tashkent State University of Economics |
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| Cites_doi | 10.1134/S1995080221030161 10.1134/S1995080222060257 10.1016/0022-1236(80)90085-3 10.1134/S1995080222140074 10.1016/S0034-4877(13)60004-X 10.1007/s00220-005-1454-y 10.1007/s11232-008-0064-1 10.1134/S1995080222150173 10.1007/978-3-642-66282-9 10.1088/1751-8121/abfcf4 10.1016/0003-4916(76)90038-5 10.1134/S1995080222150161 10.1134/S1995080222150112 10.1016/S0034-4877(10)00004-2 10.1103/RevModPhys.58.361 10.1134/S1995080222150082 10.1016/0003-4916(77)90015-X |
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| Keywords | symmetric Laplace operator energy operator two-particle quantum system 2010 Mathematics Subject Classification: 81Q10, 35P20, 47N50 eigenvalue eigenfunction |
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| SubjectTerms | Algebra Analysis Eigenvalues Eigenvectors Geometry Laplace transforms Mathematical Logic and Foundations Mathematics Mathematics and Statistics Operators (mathematics) Probability Theory and Stochastic Processes Quantum theory Schrodinger equation |
| Title | On the Spectrum of the Two-Particle Schrödinger Operator with Point Potential: Two Dimensional Case |
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