An energy spectrum is a distribution of energy among a large assemblage of particles. It is a statistical representation of the wave energy as a function of the wave frequency, and an empirical estimator of the spectral function. For any given value of energy, it determines how many of the particles have that much energy.

The particles may be atoms, photons or a flux of elementary particles.

The Schrödinger equation and a set of boundary conditions form an eigenvalue problem. A possible value (E) is called an eigenenergy. A non-zero solution of the wave function is called an eigenenergy state, or simply an eigenstate. The set of eigenvalues {Ej} is called the energy spectrum of the particle.

The electromagnetic spectrum can also be represented as the distribution of electromagnetic radiation according to energy as well. the relationship among the wavelength (usually denoted by Greek "lambda"), the frequency (usually denoted by Greek "nu"), and the energy E are:

E=h?=hc/?

where c is the speed of light and h is Planck's Constant.

An example of an energy spectrum in the physical domain is ocean waves breaking on the shore. For any given interval of time it can be observed that some of the waves are larger than others. Plotting the number of waves against the amplitude (height) for the interval will yield the energy spectrum of the set.