Bound States of a System of Two Fermions on Invariant Subspace

Abstract

We consider a Hamiltonian of a system of two fermions on a three-dimensional lattice Z 3 with special potential . The corresponding Shrödinger operator H ( k ) of the system has an invariant subspac L - 123 (T 3 ) , where we study the eigenvalues and eigenfunctions of its restriction H - 123 ( k ) . Moreover, there are shown that H - 123 ( k 1 , k 2 , π) has also infinitely many invariant subspaces , where the eigenvalues and eigenfunctions of eigenvalue problem are explicitly found.