# Spontaneous emission

The spontaneous emission , also called quantum emission in older literature , is a quantum mechanical phenomenon. It describes the emission of photons when transitioning between states of atoms or molecules with different energies . In contrast to the stimulated emission , the spontaneous emission takes place without external influence, so it belongs to the decay processes and the random processes .

## description

The exact point in time at which an energetically excited system emits a photon cannot be predicted. Instead, quantum physics only allows the specification of a probability that an emission will take place within a certain period of time. It can be characterized, for example, via the half-life after which just half of the particles in an ensemble of excited atoms or molecules have each emitted a photon, or over the life of the excited state.

In the context of quantum mechanics, which among other things describes the structure of atoms and molecules, the absorption of a photon and its stimulated emission can be well understood; Both are triggered by the radiation of an electromagnetic wave and only differ in their mathematical description by one sign . The spontaneous emission, on the other hand, is initially not to be understood; Contrary to intuition , according to the rules of quantum mechanics, in the absence of external disturbances, a state of higher energy is also stable.

The mechanism of spontaneous emission was therefore only understood in the context of quantum electrodynamics , which can also describe the generation and annihilation of photons. After that, the vacuum is filled with certain vacuum fluctuations of the electromagnetic field . These vibrations correspond to its basic energetic state and therefore cannot be destroyed by absorption in principle. The phenomenon of spontaneous emission can now be qualitatively and quantitatively traced back to a stimulated emission that is triggered by these vacuum fluctuations.

## Mathematical description

The number of spontaneous emissions or the excited particles per volume  and time  is proportional to the particle number density in the excited state : ${\ displaystyle N}$${\ displaystyle V}$${\ displaystyle t}$ ${\ displaystyle n}$

${\ displaystyle {\ frac {\ partial N} {\ partial t}} \ propto n \ cdot V}$

However, if there is a sufficient amount of particles, emitted photons will be absorbed by non-excited particles; H. Emission and absorption are in balance. This means that the intensity (including the stimulated emission) is not exceeded according to the Planck formula and the total intensity is therefore independent of the number of particles.

## Individual evidence

1. Albert Einstein: On the quantum theory of radiation . In: Physical Society Zurich. Notifications . tape 16 , 1916, pp. 47-62 .
2. Albert Einstein: On the quantum theory of radiation . In: Physikalische Zeitschrift . tape 18 , 1917, pp. 121-128 .
3. D. Meschede: Gerthsen Physik . 23rd edition. S. 577 .