Discrete spectrum (physics)

A physical quantity is said to have a discrete spectrum if it takes only distinct values, with positive gaps between one value and the next.

The classical example of discrete spectrum (for which the term was first used) is the characteristic set of discrete spectral lines seen in the emission spectrum and absorption spectrum of isolated atoms of a chemical element, which only absorb and emit light at particular wavelengths. The technique of spectroscopy is based on this phenomenon.

Discrete spectra are contrasted with the continuous spectra also seen in such experiments, for example in thermal emission, in synchrotron radiation, and many other light-producing phenomena.

Discrete spectra are seen in many other phenomena, such as vibrating strings, microwaves in a metal cavity, sound waves in a pulsating star, and resonances in high-energy particle physics.

The general phenomenon of discrete spectra in physical systems can be mathematically modeled with tools of functional analysis, specifically by the decomposition of the spectrum of a linear operator acting on a functional space.