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emission of photons
Consider an atom, in which an electron is in a superposition of two quantum statesinternal link of different energy. The wavefunction of the electron is then the sum of the wavefunctions of the two states of definite energy, which then oscillates with a frequency proportional to the energy difference between the two statesinternal link. The movie shows the oscillating probability distribution of the hydrogen atom’s only electron in the superposition of the 1S ground state and the higher-energy 2P state.
Oscillating electrons in a superposition state of hydrogen 1S and 2P radiate electromagnetic waves.
Because the electron carries a charge, its oscillating probability distribution implies the oscillation of charge. As a consequence, a tiny antenna is formed! This antenna can receive and radiate electromagnetic waves just as a radio antenna, with the only difference that the atomic antenna can oscillate much faster and hence receive and radiate much faster oscillating waves, i.e. light waves instead of radio waves. These oscillations are usually created in a large number of atoms simultaneously. Light is radiated out or swallowed by this ensemble of oscillating atomic dipole antennas in quanta: by the emission or absorption of a photon, respectively. Each time a photon is emitted or absorbed, an electron jumps from higher to lower, or from lower to higher energy state in one of the atoms, respectivley.
According to the laws of quantum theoryinternal link, the atomic antennas oscillate at a frequency of
f=\Delta W / h,
where \Delta W = W_2 -W_1, the energy difference between the participating quantum states. The energy of the emitted photons is given by
W_{ph}=h\,f,

The two equations yield
W_{ph}=\Delta W,
that is, the energy of the emitted photon is equal to the energy difference between the two quantum states. Hence, energy is conserved upon the emission or absorption of a photon, because the energy of the emitting or absorbing atom is reduced or enhanced by the photon energy, respectively.