Semirelativistic few body problems with matrix continued fraction methods

In this thesis I will present a formalism that allows for an asymptotically exact solution for both nonrelativistic and semirelativistic few body problems. First we will look at the two body problem with infinitely rising confining potentials. We will consider linear and quadratic confinement. Next we will move on to the three body problem and present a method that allows us to solve the Faddeev integral equations of the semirelativistic constituent quark model. Similar to the two body problem we will model the three quark interaction by an infinitely rising confining potential. We will also show how by exploiting symmetries in the three body problem we are able to solve the Faddeev equations resulting in the energies for several different constituent quark models that match with experimental data taken by the Particle Data Group.