Bound states of the system of two fermions on the three-dimensional lattice

Algebra, Analysis and Quantum Probability

Abdullayev, Janikul^1 ; Mamirov, Berdiyor^1

Samarkand State University, Samarkand, Uzbekistan^1

关键词: Bound state;    Invariant subspace;    Three-dimensional lattices;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/697/1/012022/pdf
DOI  :  10.1088/1742-6596/697/1/012022

来源: IOP

【 摘 要 】

In this paper, the Hamiltonian of the system of two fermions on the three-dimensional lattice3is considered. Under some conditions to the potential, it is proven that H(k) has four invariant subspaces: in one of them H(k) coincides with H0(k) and the restrictions of H(k) to the rests three subspaces are unitarily equivalent to each other. Moreover, for the eigenvalues and eigenfunctions of these restricted operators explicit expressions are found.