Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2008.Includes bibliographical references (p. 91-95).This work explores the problem of distinguishing potentially interesting new exotic states in QCD from conventional scattering states using lattice QCD, and addresses the specific case of the search for localized resonances in a system of five quarks. We employ a complete basis of local interpolating operators, as well as a number of spatially distributed operators, to search for localized resonances in the system of five quarks. Motivated by initially promising experimental searches for the 8+(1540) pentaquark, we have set out to implement new approaches, both on the theoretical and computational side, to allow for calculations deemed infeasible by other groups searching for pentaquarks on the lattice. We restrict our system of five quarks to the quantum numbers of the O+(1540) pentaquark and get an insight into the structure of its states, calculate their energies and explore their properties. Finally, we use the obtained results to discriminate between scattering and exotic states. The calculation is performed in the quenched approximation with heavy Wilson fermions.by Dmitry Sigaev.Ph.D.