Estimates on the number of eigenvalues of two-particle discrete Schrödinger operators
| dc.creator | Albeverio, Sergio | |
| dc.creator | Lakaev, Saidakhmat N. | |
| dc.creator | Abdullaev, Janikul I. | |
| dc.date | 2005-01-12 | |
| dc.date.accessioned | 2026-07-07T04:31:49Z | |
| dc.date.available | 2026-07-07T04:31:49Z | |
| dc.description | Two-particle discrete Schrödinger operators $H(k)=H_{0}(k)-V$ on the three-dimensional lattice $\Z^3,$ $k$ being the two-particle quasi-momentum, are considered. An estimate for the number of the eigenvalues lying outside of the band of $H_{0}(k)$ via the number of eigenvalues of the potential operator $V$ bigger than the width of the band of $H_{0}(k)$ is obtained. The existence of non negative eigenvalues below the band of $H_{0}(k)$ is proven for nontrivial values of the quasi-momentum $k\in \T^3\equiv (-π,π]^3$, provided that the operator H(0) has either a zero energy resonance or a zero eigenvalue. It is shown that the operator $H(k), k\in \T^3,$ has infinitely many eigenvalues accumulating at the bottom of the band from below if one of the coordinates $k^{(j)},j=1,2,3,$ of $k\in \T^3$ is $π.$ | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0501036 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0501036 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57956 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Spectral Theory | |
| dc.subject | Primary: 81Q10, Secondary: 35P20, 47N50 | |
| dc.title | Estimates on the number of eigenvalues of two-particle discrete Schrödinger operators | |
| dc.type | text |