Quantization (physics)

quantizationquantizedquantizequantizingquantisationbundles of energycanonical approach to quantum mechanicsenergy quantizationfield quantumminimum length
In physics, quantization is the process of transition from a classical understanding of physical phenomena to a newer understanding known as quantum mechanics.wikipedia
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Quantum mechanics

quantum physicsquantum mechanicalquantum theory
In physics, quantization is the process of transition from a classical understanding of physical phenomena to a newer understanding known as quantum mechanics. (It is a procedure for constructing a quantum field theory starting from a classical field theory.) This is a generalization of the procedure for building quantum mechanics from classical mechanics.
Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values (quantization), objects have characteristics of both particles and waves (wave-particle duality), and there are limits to the precision with which quantities can be measured (the uncertainty principle).

Quantum

quantaquantizedquantal
Also related is field quantization, as in the "quantization of the electromagnetic field", referring to photons as field "quanta" (for instance as light quanta).
The fundamental notion that a physical property may be "quantized" is referred to as "the hypothesis of quantization".

Photon

photonslight quantaincident photon
Also related is field quantization, as in the "quantization of the electromagnetic field", referring to photons as field "quanta" (for instance as light quanta).
Although these semiclassical models contributed to the development of quantum mechanics, many further experiments beginning with the phenomenon of Compton scattering of single photons by electrons, validated Einstein's hypothesis that light itself is quantized.

Field (physics)

fieldfieldsfield theory
(It is a procedure for constructing a quantum field theory starting from a classical field theory.) This is a generalization of the procedure for building quantum mechanics from classical mechanics. Quantization converts classical fields into operators acting on quantum states of the field theory. The classical field is treated as a dynamical variable called the canonical coordinate, and its time-derivative is the canonical momentum.
For example, quantizing classical electrodynamics gives quantum electrodynamics.

Canonical quantization

field operatorcanonicalfield operators
The first method to be developed for quantization of field theories was canonical quantization.
In physics, canonical quantization is a procedure for quantizing a classical theory, while attempting to preserve the formal structure, such as symmetries, of the classical theory, to the greatest extent possible.

BRST quantization

BRSTBRST formalismBRST theory
It involves the Batalin–Vilkovisky formalism, an extension of the BRST formalism.
In theoretical physics, the BRST formalism, or BRST quantization (where the BRST refers to Becchi, Rouet, Stora and Tyutin) denotes a relatively rigorous mathematical approach to quantizing a field theory with a gauge symmetry.

Loop quantum gravity

Loop gravitycovariant quantum gravityQuantum Graph Theory
See Loop quantum gravity.
To do this, in LQG theory space and time are quantized analogously to the way quantities like energy and momentum are quantized in quantum mechanics.

Quantum number

quantum numbersq-number3d, 4d, and 5d
An important aspect of quantum mechanics is the quantization of many observable quantities of interest.

Path integral formulation

path integralFeynman path integralpath integrals
A quantum-mechanical description of the classical system can also be constructed from the action of the system by means of the path integral formulation.
Feynman showed that this formulation of quantum mechanics is equivalent to the canonical approach to quantum mechanics when the Hamiltonian is at most quadratic in the momentum.

Quantum Hall effect

von Klitzing constantquantum Hallinteger quantum Hall effect
The integer quantization of the Hall conductance was originally predicted by University of Tokyo researchers Tsuneya Ando, Yukio Matsumoto and Yasutada Uemura in 1975, on the basis of an approximate calculation which they themselves did not believe to be true.

Physics

physicistphysicalphysicists
In physics, quantization is the process of transition from a classical understanding of physical phenomena to a newer understanding known as quantum mechanics.

Quantum field theory

quantum field theoriesquantum fieldquantum theory
(It is a procedure for constructing a quantum field theory starting from a classical field theory.) This is a generalization of the procedure for building quantum mechanics from classical mechanics.

Classical mechanics

Newtonian mechanicsNewtonian physicsclassical
(It is a procedure for constructing a quantum field theory starting from a classical field theory.) This is a generalization of the procedure for building quantum mechanics from classical mechanics.

Electromagnetic field

electromagnetic fieldselectromagneticEMF
Also related is field quantization, as in the "quantization of the electromagnetic field", referring to photons as field "quanta" (for instance as light quanta).

Particle physics

high energy physicsparticle physicisthigh-energy physics
This procedure is basic to theories of particle physics, nuclear physics, condensed matter physics, and quantum optics.

Nuclear physics

nuclear physicistnuclearnuclear science
This procedure is basic to theories of particle physics, nuclear physics, condensed matter physics, and quantum optics.

Condensed matter physics

condensed matterCondensed matter theorycondensed-matter physics
This procedure is basic to theories of particle physics, nuclear physics, condensed matter physics, and quantum optics.

Quantum optics

quantum electronicsquantum opticalquantum-optical
This procedure is basic to theories of particle physics, nuclear physics, condensed matter physics, and quantum optics.

Quantum state

eigenstatepure stateeigenstates
Quantization converts classical fields into operators acting on quantum states of the field theory.

Vacuum state

quantum vacuumvacuumZero-point field
The lowest energy state is called the vacuum state.

Probability amplitude

probability densityBorn probabilitytransition amplitude
The reason for quantizing a theory is to deduce properties of materials, objects or particles through the computation of quantum amplitudes, which may be very complicated.

Renormalization

renormalizablerenormalisationrenormalized
Such computations have to deal with certain subtleties called renormalization, which, if neglected, can often lead to nonsense results, such as the appearance of infinities in various amplitudes.

Canonical coordinates

conjugate momentacanonical momentumconjugate momentum
The classical field is treated as a dynamical variable called the canonical coordinate, and its time-derivative is the canonical momentum.