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In quantum mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
, a doublet is a composite quantum state of a system with an effective spin 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
In quantum mechanics, a two-state system (also known as a two-level system) is a quantum system that can exist in any quantum superposition of two independent (physically distinguishable) quantum states. The Hilbert space describing such a syste ...
s. Essentially all occurrences of doublets in nature arise from rotational symmetry
Rotational symmetry, also known as radial symmetry in geometry, is the property a shape (geometry), shape has when it looks the same after some rotation (mathematics), rotation by a partial turn (angle), turn. An object's degree of rotational s ...
; spin 1/2 is associated with the fundamental representation of the Lie group
In mathematics, a Lie group (pronounced ) is a group (mathematics), group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable.
A manifold is a space that locally resembles Eucli ...
SU(2).
History and applications
The term "doublet" dates back to the early 19th century, when it was observed that certain spectral lines of an ionized, excited gas would split into two under the influence of a strongmagnetic field
A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular ...
, 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 is the field of study that measures and interprets electromagnetic spectra. In narrower contexts, spectroscopy is the precise study of color as generalized from visible light to all bands of the electromagnetic spectrum.
Spectro ...
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
The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
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 is an Intrinsic and extrinsic properties, intrinsic form of angular momentum carried by elementary particles, and thus by List of particles#Composite particles, composite particles such as hadrons, atomic nucleus, atomic nuclei, and atoms. S ...
for greater detail.
Doublets continue to play an important role in physics. For example, the healthcare
Health care, or healthcare, is the improvement or maintenance of health via the preventive healthcare, prevention, diagnosis, therapy, treatment, wikt:amelioration, amelioration or cure of disease, illness, injury, and other disability, physic ...
technology of magnetic resonance imaging
Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to generate pictures of the anatomy and the physiological processes inside the body. MRI scanners use strong magnetic fields, magnetic field gradients, and ...
is based on nuclear magnetic resonance. In this technology, a spectroscopic doublet occurs in a spin-1/2 atomic nucleus
The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford at the Department_of_Physics_and_Astronomy,_University_of_Manchester , University of Manchester ...
, 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. The strength and frequency of the emitted radio waves allow the concentration of such nuclei to be measured. Another potential application is the use of doublets as the emitting layer in light-emitting diode
A light-emitting diode (LED) is a semiconductor device that emits light when current flows through it. Electrons in the semiconductor recombine with electron holes, releasing energy in the form of photons. The color of the light (corre ...
s (LEDs). These materials have the advantage of having 100% theoretical quantum efficiency based on spin statistics whereas singlet systems and triplet systems have significantly lower efficiencies or rely on noble metals such as Pt and Ir to emit light.
See also
*Singlet state
In quantum mechanics, a singlet state usually refers to a system in which all electrons are paired. The term 'singlet' originally meant a linked set of particles whose net angular momentum is zero, that is, whose overall spin quantum number s=0. A ...
* Triplet state
In quantum mechanics, a triplet state, or spin triplet, is the quantum state of an object such as an electron, atom, or molecule, having a quantum spin ''S'' = 1. It has three allowed values of the spin's projection along a given axis ''m''S = � ...
* Spin multiplicity
References
* {{DEFAULTSORT:Doublet State Spectroscopy Rotational symmetry Quantum states