physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

, a continuous spectrum usually means a set of attainable values for some

physical quantity A physical quantity is a physical property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a ' Numerical value ' and a ' Unit '. For examp ...

(such as

energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...

wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...

) that is best described as an interval of

real number In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every real ...

s, as opposed to a

discrete spectrum A physical quantity is said to have a discrete spectrum if it takes only distinct values, with 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 d ...

, a set of attainable values that is

discrete Discrete may refer to: *Discrete particle or quantum in physics, for example in quantum theory * Discrete device, an electronic component with just one circuit element, either passive or active, other than an integrated circuit *Discrete group, a ...

in the mathematical sense, where there is a positive gap between each value and the next one. The classical example of a continuous spectrum, from which the name is derived, is the part of the

spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors i ...

of the light emitted by excited

atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, and ...

s of

hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, an ...

that is due to free

electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...

s becoming bound to a hydrogen ion and emitting photons, which are smoothly spread over a wide range of wavelengths, in contrast to the discrete lines due to electrons falling from some bound

quantum state In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in ...

to a state of lower energy. As in that classical example, the term is most often used when the range of values of a physical quantity may have both a continuous and a discrete part, whether at the same time or in different situations. In

quantum system Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...

s, continuous spectra (as in

bremsstrahlung ''Bremsstrahlung'' (), from "to brake" and "radiation"; i.e., "braking radiation" or "deceleration radiation", is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typicall ...

and

thermal radiation Thermal radiation is electromagnetic radiation generated by the thermal motion of particles in matter. Thermal radiation is generated when heat from the movement of charges in the material (electrons and protons in common forms of matter) is ...

) are usually associated with free particles, such as atoms in a gas, electrons in an

electron beam Cathode rays or electron beam (e-beam) are streams of electrons observed in discharge tubes. If an evacuated glass tube is equipped with two electrodes and a voltage is applied, glass behind the positive electrode is observed to glow, due to ele ...

, or

conduction band In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies in w ...

electrons in a

metal A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typicall ...

. In particular, the

position Position often refers to: * Position (geometry), the spatial location (rather than orientation) of an entity * Position, a job or occupation Position may also refer to: Games and recreation * Position (poker), location relative to the dealer * ...

and

momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...

of a free particle has a continuous spectrum, but when the particle is confined to a limited space its spectrum becomes discrete. Often a continuous spectrum may be just a convenient model for a discrete spectrum whose values are too close to be distinguished, as in the

phonon In physics, a phonon is a collective excitation in a periodic, Elasticity (physics), elastic arrangement of atoms or molecules in condensed matter physics, condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phon ...

s in a

crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...

. The continuous and discrete spectra of physical systems can be modeled in

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Defini ...

as different parts in the decomposition of the spectrum of a

linear operator In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V \to W between two vector spaces that pre ...

acting on a

function space In mathematics, a function space is a set of functions between two fixed sets. Often, the domain and/or codomain will have additional structure which is inherited by the function space. For example, the set of functions from any set into a vect ...

, such as the

Hamiltonian Hamiltonian may refer to: * Hamiltonian mechanics, a function that represents the total energy of a system * Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system ** Dyall Hamiltonian, a modified Hamiltonian ...

operator.

References

Scattering theory {{scattering-stub he:ספקטרום רציף nl:Continu spectrum pt:Espectro contínuo

See also

References