Spectral properties of a two–particle hamiltonian on a d-dimensional lattice
https://doi.org/10.17586/2220-8054-2016-7-5-880-887
Abstract
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.
Supporting agencies: This work was supported in part by the Malaysian Ministry of Education through the Research Management Centre (RMC), Universiti Teknologi Malaysia (PAS, Ref. No. PY/2014/04068, Vote: QJ130000.2726.01K82).
About the Authors
M. I. Muminov
Universiti Teknologi Malaysia (UTM)
Malaysia
Malaysia
81310 Skudai, Johor Bahru
A. M. Khurramov
Department of Mechanical and Mathematics, Samarkand State University
Uzbekistan
Uzbekistan
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Review
For citations:
Muminov M.I., Khurramov A.M. Spectral properties of a two–particle hamiltonian on a d-dimensional lattice. Nanosystems: Physics, Chemistry, Mathematics. 2016;7(5):880-887. https://doi.org/10.17586/2220-8054-2016-7-5-880-887
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