These stationary states are resonances of the quantum system. If a quantum system is excited to a high energy state, it relaxes to a lower energy state by emitting a photon into the electromagnetic field. The energy of the emitted is equal to the difference in the state energies. The natural oscillation frequency of the photon is equal to the difference in the natural frequencies of the states. The energy and osciallation frequency are related by Planck's constant, that is , where is the photon energy, is the radial frequency and is Planck's constant.
Temporal frequency is a natural and fundamental aspect of the electromagnetic field.
As discussed in lecture 6, different colors correspond to different temporal frequencies in the field. Objects are different colors because they are formed of materials with different quantum resonance frequencies. Excited gases tend emit narrow spectral ranges associated with their fundamental resonances. Spectral ranges emitted by solids tend to be more complex because quantum states broaden in dense arrays of coupled atoms. Since photons are emitted at specific frequencies rather than as arbitrary temporal functions, it is extremely difficult to precisely control the temporal structure of the optical field.