Our progress in computing the spectrum of excited baryons and mesons in lattice QCD is described. Sets of spatially-extended hadron operators with a variety of different momenta are used. A new method of stochastically estimating the low-lying effects of quark propagation is utilized which allows reliable determinations of temporal correlations of both single-hadron and multi-hadron operators. The method is tested on the isoscalar mesons in the scalar, pseudoscalar, and vector channels, and on the two-pion system of total isospin I=0,1,2.
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