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A theoretical model is introduced for constructing the vibrationalHamiltonian of Hydrogen-like atoms (HLA). The Hamiltonian is then used toderive the vibrational motion equations of HLA in Heisenberg picture. TheLangevin equation will ultimately be formed after adding the dissipative termand fluctuating (Langevin) force according to the fluctuation-dissipationtheorem (FDT). The positional noise flux is then defined as the correlationfunction of fluctuations that happens for the electron position during itsrather fast vibrational oscillations ( ). On the other hand, the positionalfluctuations led to the fluctuations in the potential and kinetic energies ofoscillating electron so that the appearance of the potential and kinetic noisefluxes is vulnerable. The positional, potential, and kinetic noise fluxes ofoscillating electron will be determined by solving the Langevin equation infrequency domain. It is finally demonstrated that the potential and kineticnoise fluxes commonly act as an internal source for producing the externalnoise flux emitted from HLA in the form of spontaneous emission with aLorentzian profile. In contrast with all previous procedures, no ambient effecthas been involved to describe the forming mechanism of spontaneous emission forthe first time.

Calculating the noise flux of spontaneous emission radiated from  Hydrogen-like atoms by means of vibrational Hamiltonian and ignoring from  ambient effects