Thomas-Fermi quark model and techniques to improve lattice QCD calculation.

Two topics are discussed separately in this thesis. In the first part a semiclassical quark model, called the Thomas-Fermi quark model, is reviewed. After a modified approach to spin in the model is introduced, I present the calculation of the spectra of octet and decuplet baryons. The six-quark doubly strange H-dibaryon state is also investigated.

In the second part, two numerical techniques which improve latice QCD calculations are covered. The first one, which we call Polynomial-Preconditioned GMRES-DR(PP-GMRESDR), is used to speed up the calculation of large systems of linear equations in LQCD. The second one, called the Polynomial-Subtraction method, is used to help reduce the noise variance of the calculations for disconnected loops in LQCD.