TITLE:
Bound States of a System of Two Fermions on Invariant Subspace
AUTHORS:
J. I. Abdullaev, A. M. Toshturdiev
KEYWORDS:
Hamiltonian, Fermion, Bound State, Shrödinger Operator, Invariant Subspace, Total Quasi-Momentum, Eigenvalue, Birman-Schwinger Principle
JOURNAL NAME:
Journal of Modern Physics,
Vol.12 No.1,
January
14,
2021
ABSTRACT: 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.