SPIN-HAMILTONIANS BY MEANS OF HIERARCHIES OF GROUP-INDEXED ALGEBRAS .2. THE EIGENSTATES AND MATRIX-ELEMENTS OF THE SPIN-HAMILTONIAN IN THE FRAME OF THE HIERARCHY OF ALGEBRAS

In this paper we present a method of construction of the basis vectors of the hierarchy of algebras. Furthermore, a procedure for an efficie nt calculation of the matrix elements is developed. The method is appl ied for the calculation of the energy eigenvalues and eigenstates for the case of a linear ring of sixteen spins with nearest-neighbor and n ext-nearest-neighbor interactions. The numerical results for the neare st-neighbor interaction are compared with those already calculated by other authors and are found to coincide.