Abstarct: Determination structure function of Hadrons is one of the most important Physical problems in QCD. In this thesis, we study the mass spectrum and decay properties of mesons in the non-relativistic potential model. Therefore, we propose new potential models for mesons interactions such as combination of Kratzer, Yukawa and Linear potentials and combination of Kratzer, Gausian and Linear potentials. To investigate agreement of our considering potential model with hadron systems, we use Cornell potential. In the following, we use perturbation method and find wavefunction of system because of its importance and application to obtain the mass spectrum, the decay constant, the leptonic and semileptonic decay width of mesons in the non-relativistic frxamework. Studying time-dependent quantum systems is interesting issues because of their usage in physics. Many of interesting quantum mechanics effect are related to this concept. Here are investigated a one-dimensional Schrödinger equation with the subject of time dependent boundary conditions for particle without spin in a finite potential well, and then we study relativistic particles by using Klein-Gordon equations and analyzed them in moving potential (potential barrier with moving wall). To show application of a time-dependent potential we are assumed a particle is trapped in a one-dimensional box and one of the wall is movable. This quantum system acts like a Stirling heat engines and we calculate it's important performance parameters. At first to investigate the decay width of a time-dependent system,we must porpose a time-dependent potential and then by using the Fermi-Golden-Rule we obtain relation between the decay width and Half-Life of the system. For example we calculate the decay width of Hydrogen atom. Then we express the general form to obtain the decay width of time-dependent systems by using the resonant state. The differential, partial and total decay widths associated with the decay of resonant state to continuum of stable sates are introduced. And when resonant has different decay modes we will be obtain corresponding the partial decay width and branching fraction. In the approximation that resonant is sharp, we see the differential and total decay width of a resonant state is such as the Fermi-Golden-Rule. Also we compare the (dimensionless) partial decay constants with the partial decay width.