Abstarct: The potential model is still one of the most challenging models in theoretical nuclear and particle physics. The most important, and probably the most difficult part ingredient of model, is to obtain the solutions of the equation under a successful potential. Till now, many works have been done on the famous equations of nonrelativistic and relativistic quantum mechanics, namely the Schrödinger, Dirac and Klein-Gordon equations. Within this thesis, we will consider the DKP and spinless Salpeter equations which have not sufficiently discussed despite their interesting structures. The former is capable of investigating both spin-zero (which is our topics) and spin-one particles. The second equation, which is derived from the Bethe-Salpeter equation after some approximations, has a semi-relativistic nature and will be introduced in a two-body basis. We first solve these equations by pure-analytical techniques under successful phenomenological potentials including exponential, coulomb, Hulthen, Woods-Saxon, Yukawa and Cornell, and thereby investigate some spin-zero bosons.