{"title":"一维晶格上模型算子特征值的数目","authors":"A. Imomov, I. Bozorov, A. Khurramov","doi":"10.17223/19988621/78/2","DOIUrl":null,"url":null,"abstract":"A model operator hμ(k), k∈(-π,π], corresponding to the Hamiltonian of a system of two arbitrary quantum particles on a one-dimensional lattice with a special dispersion function is considered. The function describes the transfer of a particle from site to sites interacting using a short-range attraction potential νμ, μ = (μ0,μ1,μ2,μ3) ∈ ℝ+4. The detailed descriptions of changes in the number of eigenvalues of the energy operator hμ(k), k∈(-π,π], relative to values of the particle interaction vector and the total quasi-momentum k ∈ Т of the system of two particles is presented.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the number of eigenvalues of a model operator on a one-dimensional lattice\",\"authors\":\"A. Imomov, I. Bozorov, A. Khurramov\",\"doi\":\"10.17223/19988621/78/2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A model operator hμ(k), k∈(-π,π], corresponding to the Hamiltonian of a system of two arbitrary quantum particles on a one-dimensional lattice with a special dispersion function is considered. The function describes the transfer of a particle from site to sites interacting using a short-range attraction potential νμ, μ = (μ0,μ1,μ2,μ3) ∈ ℝ+4. The detailed descriptions of changes in the number of eigenvalues of the energy operator hμ(k), k∈(-π,π], relative to values of the particle interaction vector and the total quasi-momentum k ∈ Т of the system of two particles is presented.\",\"PeriodicalId\":43729,\"journal\":{\"name\":\"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17223/19988621/78/2\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17223/19988621/78/2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
On the number of eigenvalues of a model operator on a one-dimensional lattice
A model operator hμ(k), k∈(-π,π], corresponding to the Hamiltonian of a system of two arbitrary quantum particles on a one-dimensional lattice with a special dispersion function is considered. The function describes the transfer of a particle from site to sites interacting using a short-range attraction potential νμ, μ = (μ0,μ1,μ2,μ3) ∈ ℝ+4. The detailed descriptions of changes in the number of eigenvalues of the energy operator hμ(k), k∈(-π,π], relative to values of the particle interaction vector and the total quasi-momentum k ∈ Т of the system of two particles is presented.