Abstract
The method of double-time Green's functions is used to study the excitation spectrum of an isotropic spin-one system with quadrupolar coupling. It is shown that the random-phase approximation leads to a violation of a spin-one identity and thus to equivocal results. A consistent theory free from ambiguities is developed. Also, exact upper and lower bounds on the ground-state energy of systems with dipolar as well as quadrupolar coupling are derived and studied.