Author(s)

J. I. Abdullaev, A. M. Toshturdiev^*

Samarkand State University, University Boulevard 15, Samarkand, Uzbekistan.

We consider a Hamiltonian of a system of two fermions on a three-dimensional lattice Z³ with special potential . The corresponding Shrödinger operator H(k) of the system has an invariant subspac L^-₁₂₃(T³) , where we study the eigenvalues and eigenfunctions of its restriction H^-₁₂₃(k). Moreover, there are shown that H^-₁₂₃(k₁, k₂, π) has also infinitely many invariant subspaces , where the eigenvalues and eigenfunctions of eigenvalue problem are explicitly found.

Hamiltonian, Fermion, Bound State, Shrödinger Operator, Invariant Subspace, Total Quasi-Momentum, Eigenvalue, Birman-Schwinger Principle

Abdullaev, J. and Toshturdiev, A. (2021) Bound States of a System of Two Fermions on Invariant Subspace. Journal of Modern Physics, 12, 35-49. doi: 10.4236/jmp.2021.121004.