INVERSE FORMULATION OF THE GREEN'S FUNCTION THEORY: EXACT SOLUTION FOR THE BETHE LATTICE

We study the tight-binding Hamiltonian H=∑j|j> ∊j Vjk } as controlling (prescribed) variables. Namely: (i) the inverse profile relation, i.e. z-∊j versus diagonal matrix elements, is obtained in a local form; (ii) the off-diagonal matrix elements { } are shown to exhibit a simple factorization property in terms of the diagonal ones.