Due to decay, an unstable quantum-mechanical system cannot be in the eigenstate of the Hamiltonian. Effectively, this means that the system is described by a wave-packet which ranges over a distribution of energies (or frequencies, as in the field of spectroscopy). In the simplest model of an exponential decay, the distribution of energies is given by so called Breit-Wigner distribution (and to some extent this is true for most short-living metastable system, e.g. resonances in high energy physics).

Given some quantities $E_0$ and $\Gamma$ of the dimension of energy the Breit-Wigner energy distribution

which should be in principle damped all the way to $0$ from some energy $E_{min}$ as the spectrum of any Hamiltonian must be bounded below. The plot of the Breit-Wigner curve as seen in spectroscopy is often called Breit-Wigner curve.

Various effects in nature lead to modifed, asymmetric and other spectral curves to which the Breit-Wigner is merely the crudest approximation.

Literature

Classical Breit-Wigner

Anthony Sudbery, Quantum mechanics and the particles of nature, formula 3.237 and around.

G. Breit, E. Wigner, Phys. Rev. 49, 519 (1936).

Corrected curves

Assymetric line shapes in autoionization and Rydberg atoms are studied in the famous

Ugo Fano, Effects of configuration interaction on intensities and phase shifts, Phys. Rev. 124, 1866 (1961) doi

A. Bianconi, Ugo Fano and shape resonances in X-ray and Inner Shell Processes AIP Conference Proceedings (2002): (19th Int. Conference Roma June 24–28, 2002) cond-mat/0211452

VV Sokolov, VG Zelevinsky, Dynamics and statistics of unstable quantum states, Nuclear Physics A504:3 (1989) 562-588 doi; Simple mode on a highly excited background: Collective strength and damping in the continuum, Phys. Rev. C 56, 311 (1997)