Hydrogen atom mass spectrum in the excited states

Calculation and analysis of energy spectrum in Coulomb potential of atomic systems, and hadrons in relativistic conditions due to requirements of using higher grades of relativistic corrections have attracted physics theoreticians. The ability to create mono-electron ions of heavy, semi-heavy, strange atoms and/or hadrons atoms in laboratory conditions has boomed the need of more precise and meticulous corrections. One of these factors is to determine electron mass and recoil effect of core in this system. Perturbative and variation theories, regardless of recoil effect, have been calculated in this way so far. The method presented in this paper considers recoil effect intervening and without considering that it researches energy spectrum, mass, and constituent mass in the system. To make more sense of the calculations, hydrogen atomic system has been studied to pave calculation methods for other atoms and systems including quarks, glueball, and pomeron which can be over- generalized using the intended potential.