On the Spectrum of the Two-Particle Schrödinger Operator with Point Potential: Two Dimensional Case

• Published in: Lobachevskii journal of mathematics Vol. 46; no. 1; pp. 456 - 463
• Main Author: Kuljanov, U. N.
• Format: Journal Article
• Language: English
• 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
• ISSN: 1995-0802; 1818-9962
• DOI: 10.1134/S1995080224608105

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...