  A method is presented for calculating binding energies and other properties
of extended interacting systems using the projected density of transitions
(PDoT) which is the probability distribution for transitions of different
energies induced by a given localized operator, the operator on which the
transitions are projected. It is shown that the transition contributing to the
PDoT at each energy is the one which disturbs the system least, and so, by
projecting on appropriate operators, the binding energies of equilibrium
electronic states and the energies of their elementary excitations can be
calculated. The PDoT may be expanded as a continued fraction by the recursion
method, and as in other cases the continued fraction converges exponentially
with the number of arithmetic operations, independent of the size of the
system, in contrast to other numerical methods for which the number of
operations increases with system size to maintain a given accuracy. These
properties are illustrated with a calculation of the binding energies and
zone-boundary spin- wave energies for an infinite spin-1/2 Heisenberg chain,
which is compared with analytic results for this system and extrapolations from
finite rings of spins.
