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Quarks are the only elementary particles in the Standard Model of particle physics to experience all four fundamental interactions, also known as fundamental forces (electromagnetism, gravitation, strong interaction, and weak interaction), as well as the only known particles whose electric charges are not integer multiples of the elementary charge. There are six types of quarks, known as flavors: up, down, strange, charm, top, and bottom, Up and down quarks have the lowest masses of all quarks. Bound state system is composed of quark and anti quark, due to the confinement theory, asymptotic freedom, physical structure and properties of quarks; we choose potentials according to that, the potentials are harmonic, an-harmonic oscillator and Coulomb potentials .We use a method of the Eigen value problem by asymptotic iteration to find the eigenvalues of the c c bar and b b bar systems.