On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice
On three-dimensional lattice we consider a system of three quantum particles (two of them are identical (fermions) and the third one is of another nature) that interact with the help of paired short-range gravitational potentials. We prove the finiteness of a number of bound states of respective Sch...
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| Format: | Article |
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Allerton Press Incorporation
2016
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| _version_ | 1796861705123266560 |
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| author | Muminov, M. E. Shermatova, Y. M. |
| author_facet | Muminov, M. E. Shermatova, Y. M. |
| author_sort | Muminov, M. E. |
| collection | ePrints |
| description | On three-dimensional lattice we consider a system of three quantum particles (two of them are identical (fermions) and the third one is of another nature) that interact with the help of paired short-range gravitational potentials. We prove the finiteness of a number of bound states of respective Schrödinger operator in a case, when potentials satisfy some conditions and zero is a regular point for two-particle sub-Hamiltonian. We find a set of values for particles masses values such that Schrödinger operator may have only finite number of eigenvalues lying to the left of essential spectrum. |
| first_indexed | 2024-03-05T20:00:28Z |
| format | Article |
| id | utm.eprints-70094 |
| institution | Universiti Teknologi Malaysia - ePrints |
| last_indexed | 2024-03-05T20:00:28Z |
| publishDate | 2016 |
| publisher | Allerton Press Incorporation |
| record_format | dspace |
| spelling | utm.eprints-700942017-11-22T00:45:13Z http://eprints.utm.my/70094/ On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice Muminov, M. E. Shermatova, Y. M. QA Mathematics On three-dimensional lattice we consider a system of three quantum particles (two of them are identical (fermions) and the third one is of another nature) that interact with the help of paired short-range gravitational potentials. We prove the finiteness of a number of bound states of respective Schrödinger operator in a case, when potentials satisfy some conditions and zero is a regular point for two-particle sub-Hamiltonian. We find a set of values for particles masses values such that Schrödinger operator may have only finite number of eigenvalues lying to the left of essential spectrum. Allerton Press Incorporation 2016 Article PeerReviewed Muminov, M. E. and Shermatova, Y. M. (2016) On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice. Russian Mathematics, 60 (1). pp. 22-29. ISSN 1066-369X http://dx.doi.org/10.3103/S1066369X16010035 DOI:10.3103/S1066369X16010035 |
| spellingShingle | QA Mathematics Muminov, M. E. Shermatova, Y. M. On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice |
| title | On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice |
| title_full | On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice |
| title_fullStr | On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice |
| title_full_unstemmed | On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice |
| title_short | On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice |
| title_sort | on finiteness of discrete spectrum of three particle schrodinger operator on a lattice |
| topic | QA Mathematics |
| work_keys_str_mv | AT muminovme onfinitenessofdiscretespectrumofthreeparticleschrodingeroperatoronalattice AT shermatovaym onfinitenessofdiscretespectrumofthreeparticleschrodingeroperatoronalattice |