On the spectrum of the three-particle Hamiltonian on a unidimensional lattice
On a unidimensional lattice, the Hamiltonian of a system of three arbitrary particles is considered (with dispersion relations), where the particles interact pairwise via zero-range (contact) attractive potentials.We prove that the discrete spectrum of the corresponding Schrödinger operator is finit...
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2015
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my.utm.586872021-12-06T03:02:26Z http://eprints.utm.my/id/eprint/58687/ On the spectrum of the three-particle Hamiltonian on a unidimensional lattice Aliev, N. M. Muminov, Mukhiddin É. QA Mathematics On a unidimensional lattice, the Hamiltonian of a system of three arbitrary particles is considered (with dispersion relations), where the particles interact pairwise via zero-range (contact) attractive potentials.We prove that the discrete spectrum of the corresponding Schrödinger operator is finite for all values of the total quasimomentum if the masses of two particles are finite. We also prove that the discrete spectrum of the Schrödinger operator is infinite if the masses of two particles in a three-particle system are infinite. Allerton Press Incorporation 2015 Article PeerReviewed Aliev, N. M. and Muminov, Mukhiddin É. (2015) On the spectrum of the three-particle Hamiltonian on a unidimensional lattice. Siberian Advances in Mathematics, 25 (3). pp. 155-168. ISSN 1055-1344 http://dx.doi.org/10.3103/S1055134415030013 DOI:10.3103/S1055134415030013 |
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QA Mathematics Aliev, N. M. Muminov, Mukhiddin É. On the spectrum of the three-particle Hamiltonian on a unidimensional lattice |
| description |
On a unidimensional lattice, the Hamiltonian of a system of three arbitrary particles is considered (with dispersion relations), where the particles interact pairwise via zero-range (contact) attractive potentials.We prove that the discrete spectrum of the corresponding Schrödinger operator is finite for all values of the total quasimomentum if the masses of two particles are finite. We also prove that the discrete spectrum of the Schrödinger operator is infinite if the masses of two particles in a three-particle system are infinite. |
| format |
Article |
| author |
Aliev, N. M. Muminov, Mukhiddin É. |
| author_facet |
Aliev, N. M. Muminov, Mukhiddin É. |
| author_sort |
Aliev, N. M. |
| title |
On the spectrum of the three-particle Hamiltonian on a unidimensional lattice |
| title_short |
On the spectrum of the three-particle Hamiltonian on a unidimensional lattice |
| title_full |
On the spectrum of the three-particle Hamiltonian on a unidimensional lattice |
| title_fullStr |
On the spectrum of the three-particle Hamiltonian on a unidimensional lattice |
| title_full_unstemmed |
On the spectrum of the three-particle Hamiltonian on a unidimensional lattice |
| title_sort |
on the spectrum of the three-particle hamiltonian on a unidimensional lattice |
| publisher |
Allerton Press Incorporation |
| publishDate |
2015 |
| url |
http://eprints.utm.my/id/eprint/58687/ http://dx.doi.org/10.3103/S1055134415030013 |
| _version_ |
1718926034098716672 |