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 inLobachevskii journal of mathematics Vol. 46; no. 1; pp. 456 - 463
Main Author Kuljanov, U. N.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.01.2025
Springer Nature B.V
Subjects
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
symmetric Laplace operator
energy operator
two-particle quantum system
2010 Mathematics Subject Classification: 81Q10, 35P20, 47N50
eigenvalue
eigenfunction
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080224608105