Study of the fundamental interactions in the bounded states of the systems: Earth-Moon, Proton-Electron (hydrogen atom), positronium (process e- e+→e- e+), and quarkonium, ( QQ)

All The bound states of two particles such as the earth-moon system, bound by the gravitational interaction, proton-electron pe − hydrogen atom, positron-electron ( e + e − ) positronium linked by the electromagnetic interaction and quark-antiquark ( ( q q ¯ ) ) quarkonium linked by strong interaction, provide physicists with a natural laboratory to study these interactions. In this paper we review the classical theories formulated by Newton and relativist due to Einstein of gravitational interactions to study the earth-moon system. As regards the bound states ( pe − ), ( e + e − ) and ( ( q q ¯ ) ) we used Schrödinger equation to calculate the energy spectrum of these systems, as well as the Feynman diagrams at tree order to determine in some detail the Hamiltonian of these systems, known as Breit-Fermi potential. The similarities and differences between the hydrogen atom and the positronium are analyzed. The quarkonio is studied in the framework of the non-relativistic quark model (MQNR), heavy quark, where the relativistic effects are negligible, confronting the theoretical and experimental results to observe its validity.