The infiniteness of the number of eigenvalues in the gap in the essential spectrum for the three-particle Schrödinger operator on a lattice

被引：0

作者：

M. E. Muminov

机构：

[1] Alisher Navoi Samarkand State University,

来源：

Theoretical and Mathematical Physics | 2009年 / 159卷

关键词：

three-particle system on a lattice; Schrödinger operator; essential spectrum; discrete spectrum; compact operator;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We consider a system of three arbitrary quantum particles on a three-dimensional lattice that interact via attractive pair contact potentials. We find a condition for a gap to appear in the essential spectrum and prove that there are infinitely many eigenvalues of the Hamiltonian of the corresponding three-particle system in this gap.

引用

页码：667 / 683

页数：16

共 50 条

[1] The infiniteness of the number of eigenvalues in the gap in the essential spectrum for the three-particle Schrodinger operator on a lattice
Muminov, M. E.
THEORETICAL AND MATHEMATICAL PHYSICS, 2009, 159 (02) : 667 - 683
[2] Formula for the number of eigenvalues of a three-particle Schrödinger operator on a lattice
M. E. Muminov
Theoretical and Mathematical Physics, 2010, 164 : 869 - 882
[3] The Asymptotics of the Number of Eigenvalues of a Three-Particle Lattice Schrödinger Operator
S. N. Lakaev
Z. I. Muminov
Functional Analysis and Its Applications, 2003, 37 : 228 - 231
[4] The Number of Eigenvalues of the Three-Particle Schrödinger Operator on Three Dimensional Lattice
A. M. Khalkhuzhaev
J. I. Abdullaev
J. Kh. Boymurodov
Lobachevskii Journal of Mathematics, 2022, 43 : 3486 - 3495
[5] Spectrum of the Three-Particle Schrödinger Difference Operator on a Lattice
S. N. Lakaev
Zh. I. Abdullaev
Mathematical Notes, 2002, 71 : 624 - 633
[6] Essential and Discrete Spectra of the Three-Particle Schrödinger Operator on a Lattice
S. N. Lakaev
M. É. Muminov
Theoretical and Mathematical Physics, 2003, 135 : 849 - 871
[7] Essential and discrete spectra of the three-particle Schrödinger operator on a lattice
Yu. Kh. Eshkabilov
R. R. Kucharov
Theoretical and Mathematical Physics, 2012, 170 : 341 - 353
[8] On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice
Muminov M.E.
Shermatova Y.M.
Russian Mathematics, 2016, 60 (1) : 22 - 29
[9] On the Existence of Eigenvalues of the Three-Particle Discrete Schrödinger Operator
Abdullaev, J. I.
Boymurodov, J. K.
Khalkhuzhaev, A. M.
MATHEMATICAL NOTES, 2023, 114 (5-6) : 645 - 658
[10] On the Existence of Eigenvalues of the Three-Particle Discrete Schrödinger Operator
J. I. Abdullaev
J. K. Boymurodov
A. M. Khalkhuzhaev
Mathematical Notes, 2023, 114 : 645 - 658

← 1 2 3 4 5 →