  A theoretical model is introduced for constructing the vibrational
Hamiltonian of Hydrogen-like atoms (HLA). The Hamiltonian is then used to
derive the vibrational motion equations of HLA in Heisenberg picture. The
Langevin equation will ultimately be formed after adding the dissipative term
and fluctuating (Langevin) force according to the fluctuation-dissipation
theorem (FDT). The positional noise flux is then defined as the correlation
function of fluctuations that happens for the electron position during its
rather fast vibrational oscillations ( ). On the other hand, the positional
fluctuations led to the fluctuations in the potential and kinetic energies of
oscillating electron so that the appearance of the potential and kinetic noise
fluxes is vulnerable. The positional, potential, and kinetic noise fluxes of
oscillating electron will be determined by solving the Langevin equation in
frequency domain. It is finally demonstrated that the potential and kinetic
noise fluxes commonly act as an internal source for producing the external
noise flux emitted from HLA in the form of spontaneous emission with a
Lorentzian profile. In contrast with all previous procedures, no ambient effect
has been involved to describe the forming mechanism of spontaneous emission for
the first time.
