The process by which excited electrons emit photons while falling to the ground level or lower energy level is called spontaneous emission.
The electrons in the excited state do not stay for a long period because the lifetime of electrons in the higher energy state or excited state is very small, of the order of 10-8 sec. Hence, after a short period, they fall back to the ground state by releasing energy in the form of photons or light.
Ground state probability is maximum at the origin in quantum harmonic oscillator due quantum tunneling effect, while classically the probability is minimum at the origin
According to weisskopf-wigner theory on page 206 of "Quantum optics" by Marlan O. Scully and M. Suhail Zubairy .
Vacuum field modes cause spontaneous emission, which perturbs your system (particularly in the excited state), resulting in energy and time uncertainty. This uncertainty in energy will give rise to the life time of the excited state, according to the Heisenberg uncertainty relation.
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