najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2016-7-5-880-887najo-955Research ArticleСтатьиSpectral properties of a two–particle hamiltonian on a d-dimensional latticeMuminovM. I.

81310 Skudai, Johor Bahru

mmuminov@mail.ruKhurramovA. M.xurramov@mail.ruUniversiti Teknologi Malaysia (UTM)MalaysiaDepartment of Mechanical and Mathematics, Samarkand State UniversityUzbekistan20161508202575880887Copyright © Muminov M.I., Khurramov A.M., 20252025Muminov M.I., Khurramov A.M.Muminov M.I., Khurramov A.M.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/955

A system of two arbitrary quantum particles moving on d-dimensional lattice interacting via some attractive potential is considered. The number of eigenvalues of the family h(k) is studied depending on the interaction energy of particles and the total quasi-momentum k ϵTd (Td - d-dimensional torus). Depending on the interaction energy, the conditions for h(0) that has simple or multifold virtual level at 0 are found.

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The authors declare that there are no conflicts of interest present.