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In quantum mechanics
Quantum mechanics

Quantum mechanics is a set of principles underlying the most fundamental known description of all physical systems at the microscopic scale . Notable amongst these principles are both a dual wave-like and particle-like behavior of matter and radiation, and prediction of probabilities in situations where classical physics predicts certaintie...
, a doublet is a quantum state of a system with a spin
Spin (physics)

In quantum mechanics, spin is a fundamental property of atomic nucleus, hadrons, and elementary particles. For particles with non-zero spin, spin direction is an important intrinsic degrees of freedom ....
 of 1/2, such that there are two allowed values of the spin component, -1/2 and +1/2. Quantum systems with two possible states are sometimes called two-level system
Two-level system

In quantum mechanics, a two-state system is a system which has two possible states. More formally, the Hilbert space of a two state system has two degrees of freedom , so a complete basis spanning the space must consist of two independent states....
s. Essentially all occurrences of doublets in nature arise from rotational symmetry
Rotational symmetry

File:The armoured triskelion on the flag of the Isle of Man.svgGenerally speaking, an object with rotational symmetry is an object that looks the same after a certain amount of rotation....
; spin 1/2 is associated with the fundamental representation
Fundamental representation

In representation theory of Lie groups and Lie algebras, a fundamental representation is an irreducible finite-dimensional representation of a semisimple Lie group...
 of the Lie group
Lie group

In mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the Differential structure....
 SU(2), the group
Group theory

In mathematics and abstract algebra, group theory studies the algebraic structures known as group .The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring , field , and vector spaces can all be seen as groups endowed with additional operations and axioms....
 that defines rotational symmetry in three-dimensional space.

History and applications
The term "doublet" dates back to the 19th century, when it was observed that certain spectral lines of an ionized, excited gas would split into two under the influence of a strong magnetic field
Magnetic field

A magnetism field is a vector field which can exert a magnetic force on moving electric charges and on magnetic dipoles . When placed in a magnetic field, magnetic dipoles tend to align their axes parallel to the magnetic field....
, in an effect known as the anomalous Zeeman effect.






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In quantum mechanics
Quantum mechanics

Quantum mechanics is a set of principles underlying the most fundamental known description of all physical systems at the microscopic scale . Notable amongst these principles are both a dual wave-like and particle-like behavior of matter and radiation, and prediction of probabilities in situations where classical physics predicts certaintie...
, a doublet is a quantum state of a system with a spin
Spin (physics)

In quantum mechanics, spin is a fundamental property of atomic nucleus, hadrons, and elementary particles. For particles with non-zero spin, spin direction is an important intrinsic degrees of freedom ....
 of 1/2, such that there are two allowed values of the spin component, -1/2 and +1/2. Quantum systems with two possible states are sometimes called two-level system
Two-level system

In quantum mechanics, a two-state system is a system which has two possible states. More formally, the Hilbert space of a two state system has two degrees of freedom , so a complete basis spanning the space must consist of two independent states....
s. Essentially all occurrences of doublets in nature arise from rotational symmetry
Rotational symmetry

File:The armoured triskelion on the flag of the Isle of Man.svgGenerally speaking, an object with rotational symmetry is an object that looks the same after a certain amount of rotation....
; spin 1/2 is associated with the fundamental representation
Fundamental representation

In representation theory of Lie groups and Lie algebras, a fundamental representation is an irreducible finite-dimensional representation of a semisimple Lie group...
 of the Lie group
Lie group

In mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the Differential structure....
 SU(2), the group
Group theory

In mathematics and abstract algebra, group theory studies the algebraic structures known as group .The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring , field , and vector spaces can all be seen as groups endowed with additional operations and axioms....
 that defines rotational symmetry in three-dimensional space.

History and applications


The term "doublet" dates back to the 19th century, when it was observed that certain spectral lines of an ionized, excited gas would split into two under the influence of a strong magnetic field
Magnetic field

A magnetism field is a vector field which can exert a magnetic force on moving electric charges and on magnetic dipoles . When placed in a magnetic field, magnetic dipoles tend to align their axes parallel to the magnetic field....
, in an effect known as the anomalous Zeeman effect. Such spectral lines were observed not only in the laboratory, but also in astronomical spectroscopy
Spectroscopy

Spectroscopy was originally the study of the interaction between radiation and matter as a function of wavelength . In fact, historically, spectroscopy referred to the use of visible light dispersed according to its wavelength, e.g....
 observations, allowing astronomers to deduce the existence of, and measure the strength of magnetic fields around the sun, stars and galaxies. Conversely, it was the observation of doublets in spectroscopy that allowed physicists to deduce that the electron
Electron

The electron is a subatomic particle that carries a negative electric charge. It has elementary particle and is believed to be a point particle....
 had a spin, and that furthermore, the magnitude of the spin had to be 1/2. See the history section of the article on spin (physics)
Spin (physics)

In quantum mechanics, spin is a fundamental property of atomic nucleus, hadrons, and elementary particles. For particles with non-zero spin, spin direction is an important intrinsic degrees of freedom ....
 for greater detail.

Doublets continue to play an important role in physics. For example, the healthcare technology of magnetic resonance imaging
Magnetic resonance imaging

GaneshMagnetic resonance imaging , or nuclear magnetic resonance imaging , is primarily a medical imaging technique most commonly used in radiology to visualize the structure and function of the body....
 is based on nuclear magnetic resonance
Nuclear magnetic resonance

Nuclear magnetic resonance is the name given to a physical resonance phenomenon involving the observation of specific quantum mechanics magnetism properties of an atomic atomic nucleus in the presence of an applied, external magnetic field....
. In this technology, a spectroscopic doublet occurs in a spin-1/2 atomic nucleus
Atomic nucleus

The nucleus of an atom is the very dense region, consisting of nucleons , at the center of an atom. Although the size of the nucleus varies considerably according to the mass of the atom, the size of the entire atom is comparatively constant....
, whose doublet splitting is in the radio-frequency range. By applying both a magnetic field and carefully tuning a radio-frequency transmitter, the nuclear spins will flip and re-emit radiation, in an effect known as the Rabi cycle
Rabi cycle

In physics, the Rabi cycle is the cyclic behaviour of a two-state quantum system in the presence of an oscillatory driving field. A two-state system has two possible states, and if they are not degenerate energy levels the system can become "excited" when it absorbs a quantum of energy....
. The strength and frequency of the emitted radio waves allows the concentration of such nuclei to be measured.

See also

  • Singlet state
  • Triplet state
    Triplet state

    In physics, spin is the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point....
  • Spin multiplicity
    Spin multiplicity

    In quantum mechanics, spin multiplicity denotes the number of possible quantum states of a system with given principal spin quantum number S. The different states are distinguished by the spin projection quantum number Sz, which can take the values -S, -S+1, ..., S-1, S....