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Converting classical mechanics to quantum mechanics
First quantization is a procedure for converting equations of classical particle equations into quantum wave equations. The companion concept of second
First_quantization
Formulation of the quantum many-body problem
Canonical quantization First quantization Geometric quantization Quantization (physics) Schrödinger functional Scalar field theory Second quantization on Wikiversity
Second_quantization
Process in quantum mechanical theories
In physics, canonical quantization is a procedure for quantizing a classical theory, while attempting to preserve the formal structure, such as symmetries
Canonical_quantization
Systematic procedure of turning a classical theory into a quantum one
generalization involving infinite degrees of freedom is field quantization, as in the "quantization of the electromagnetic field", referring to photons as field
Quantization_(physics)
Topics referred to by the same term
Look up quantization in Wiktionary, the free dictionary. Quantization is the process of constraining an input from a continuous or otherwise large set
Quantization
Signal encoder
the quantized signal. The incorporation of the decoder inside the encoder allows quantization of the differences, including nonlinear quantization, in
Differential pulse-code modulation
Differential_pulse-code_modulation
Recipe for constructing a quantum analog of a classical physical theory
quantization is a mathematical approach to defining a quantum theory corresponding to a given classical theory. It attempts to carry out quantization
Geometric_quantization
Type of machine learning model
preserving most of its performance. Quantization can be further classified as static quantization if the quantization parameters are determined beforehand
Large_language_model
Predecessor to modern quantum mechanics (1900–1925)
orientations, so that the process of quantization does not pick out a preferred axis. For this reason, the name "space quantization" fell out of favor, and the
Old_quantum_theory
Physical model of propagating energy
sometimes known as the Planck–Einstein equation. In quantum theory (see first quantization) the energy of the photons is thus directly proportional to the frequency
Electromagnetic_radiation
Atomic model introduced by Niels Bohr in 1913
the quantized angular momentum condition of the Bohr model with an additional radial quantization condition, the Wilson–Sommerfeld quantization condition
Bohr_model
Image processing technique
In computer graphics, color quantization or color image quantization is quantization applied to color spaces; it is a process that reduces the number of
Color_quantization
Online vector quantization algorithm
searched efficiently. Earlier approaches to vector quantization include product quantization, scalar quantization, and data-dependent k-means codebook construction
TurboQuant
Continuous progression from past to future
acceleration of the observer. Time quantization refers to the theory that time has a smallest possible unit. Time quantization is a hypothetical concept. In
Time
Minimum amount of a physical entity involved in an interaction
levels within an atom. Quantization is one of the foundations of the much broader physics of quantum mechanics. Quantization of energy and its influence
Quantum
Mapping between functions in the quantum phase space
Weyl quantization. It is now understood that Weyl quantization does not satisfy all the properties one would require for consistent quantization and therefore
Wigner–Weyl_transform
Quantization giving rise to photons
function is derived from a "first" quantized Hamiltonian, the quantization of the Schrödinger field is the second time quantization is performed, hence the
Quantization of the electromagnetic field
Quantization_of_the_electromagnetic_field
Method for converting signals between digital and analog
feedback loop during quantization to the lower bit depth that continuously corrects quantization errors and moves quantization noise to higher frequencies
Delta-sigma_modulation
Quantum mechanical operator related to rotational symmetry
{\displaystyle \hbar } is reduced Planck constant: A common way to derive the quantization rules above is the method of ladder operators. The ladder operators for
Angular_momentum_operator
Charge carried by one proton or electron
the electric constant, and ħ is the reduced Planck constant. Charge quantization is the principle that the charge of any object is an integer multiple
Elementary_charge
Hypothetical particle with one magnetic pole
charge quantization has appeared. (The concept of local gauge invariance—see Gauge theory—provides a natural explanation of charge quantization, without
Magnetic_monopole
Digital video coder/decoder
the quantization stage. There, a best-effort approximation of inversion is performed. This part of the process is often called inverse quantization or
Video_codec
Noise that reduces quantization error
produce. Dither is added before any quantization or re-quantization process, in order to decorrelate the quantization noise from the input signal and to
Dither
Physical theory with fields invariant under the action of local "gauge" Lie groups
variety of means. Methods for quantization are covered in the article on quantization. The main point to quantization is to be able to compute quantum
Gauge_theory
Quantized unit of magnetic flux
from Φ0. The flux quantization is a key idea behind a SQUID, which is one of the most sensitive magnetometers available. Flux quantization also plays an important
Magnetic_flux_quantum
State of matter at low temperatures
the rotating state consists of quantized vortices. That is, when the container is rotated at speeds below the first critical angular velocity, the liquid
Superfluid_helium-4
System that converts an analog signal into a digital signal
signal. The conversion involves quantization of the input, so it necessarily introduces a small amount of quantization error. Furthermore, instead of continuously
Analog-to-digital_converter
Lossy compression technique
Specific applications include DCT data quantization in JPEG and DWT data quantization in JPEG 2000. Color quantization reduces the number of colors used in
Quantization (image processing)
Quantization_(image_processing)
Video encoding algorithm
Adaptive Quantization Not Suck". 2008-02-22. Archived from the original on 2020-08-07. Implementation of variance-based adaptive quantization in x264 The
Variance Adaptive Quantization
Variance_Adaptive_Quantization
Ratio of the desired signal to the background noise
possible noise level is the error caused by the quantization of the signal, sometimes called quantization noise. This noise level is non-linear and signal-dependent;
Signal-to-noise_ratio
Extension of the Bohr model
the quantized angular momentum condition of the Bohr model with a radial quantization (condition by William Wilson, the Wilson–Sommerfeld quantization condition):
Bohr–Sommerfeld_model
Intrinsic quantum property of particles
momentum. The relativistic spin–statistics theorem connects electron spin quantization to the Pauli exclusion principle: observations of exclusion imply half-integer
Spin_(physics)
Vector quantization algorithm minimizing the sum of squared deviations
k-means clustering is a method of vector quantization, originally from signal processing, that aims to partition n observations into k clusters in which
K-means_clustering
Force resulting from the quantisation of a field
field in question. The second quantization of quantum field theory requires that each such ball-spring combination be quantized, that is, that the strength
Casimir_effect
Number of bits of information recorded for each digital audio sample
determined by quantization error. The bit depth has no impact on the frequency response, which is constrained by the sample rate. Quantization error introduced
Audio_bit_depth
classical mechanics and result derived from Schrödinger equation. first quantization x → x ^ , p → i ℏ ∂ ∂ x {\displaystyle x\to {\hat {x}},\,p\to i\hbar
Glossary of elementary quantum mechanics
Glossary_of_elementary_quantum_mechanics
Lossy compression method for reducing the size of digital images
domain, the process of reducing information is called quantization. In simpler terms, quantization is a method for optimally reducing a large number scale
JPEG
Theoretical framework in physics
systems. The process of quantizing an arbitrary number of particles instead of a single particle is often also called second quantization. The foregoing procedure
Quantum_field_theory
Tabular arrangement of the chemical elements
number. The Danish physicist Niels Bohr applied Max Planck's idea of quantization to the atom. He concluded that the energy levels of electrons were quantised:
Periodic_table
Formulation to quantize gauge field theories in physics
relatively rigorous mathematical approach to quantizing a field theory with a gauge symmetry. Quantization rules in earlier quantum field theory (QFT)
BRST_quantization
Mathematical description of quantum state
annihilation of particles and not external potentials as in ordinary "first quantized" quantum theory. In string theory, the situation remains analogous
Wave_function
Formulation of general relativity
canonical quantization techniques for constrained Hamiltonian systems invented by Paul Dirac.[3] Dirac's approach allows the quantization of systems
Canonical_quantum_gravity
Quantum mechanics posed in terms of category theory
S.; Heunen, C. (2010). "H*-algebras and nonunital Frobenius algebras: first steps in infinite-dimensional categorical quantum mechanics". Clifford Lectures
Categorical_quantum_mechanics
1922 physical experiment demonstrating that atomic spin is quantized
to their quantized spin. Historically, this experiment was decisive in convincing physicists of the reality of angular-momentum quantization in all atomic-scale
Stern–Gerlach_experiment
Solitons in Euclidean spacetime
(Euclidean, i. e., with imaginary time) (1 + 1)-dimensional field theory – first quantized quantum mechanical description – allows to be interpreted as a tunneling
Instanton
Algebraic construct of interest in theoretical physics
though they are in some sense 'close' to a group. The term "quantum group" first appeared in the theory of quantum integrable systems, which was then formalized
Quantum_group
Quantized flux circulation of some physical quantity
Fritz London published a very closely related work on magnetic flux quantization in superconductors. London's fluxoid can also be viewed as a quantum
Quantum_vortex
deformation quantization of the corresponding Poisson algebra. It is due to Maxim Kontsevich. Given a Poisson algebra (A, {⋅, ⋅}), a deformation quantization is
Kontsevich quantization formula
Kontsevich_quantization_formula
German-born theoretical physicist (1879–1955)
received skeptically at first. In another major paper from this era, Einstein observed that de Broglie waves could explain the quantization rules of Bohr and
Albert_Einstein
contains all the information about the state of that system. This is the first quantization approach and historically Bose–Einstein and Fermi–Dirac correlations
Bose–Einstein_correlations
Theory of quantum gravity merging quantum mechanics and general relativity
{E}}_{i}^{3}{\tilde {E}}^{3i}}}.} According to the rules of canonical quantization the triads E ~ i 3 {\displaystyle {\tilde {E}}_{i}^{3}} should be promoted
Loop_quantum_gravity
Image dithering algorithm
meaning it pushes (adds) the residual quantization error of a pixel onto its neighboring pixels, to be quantized after. It spreads the debt out according
Floyd–Steinberg_dithering
Software
propagation and testing moon bounce echo. FSK441, introduced in 2001 as the first communications mode included with WSJT, is designed to support meteor scatter
WSJT_(amateur_radio_software)
Data structure in computer science
results of octree color quantization. The first image is the original (532818 distinct colors), while the second is the quantized image (184 distinct colors)
Octree
Technique in computational quantum field theory
The light-front quantization of quantum field theories provides a useful alternative to ordinary equal-time quantization. In particular, it can lead to
Light-front computational methods
Light-front_computational_methods
Digital representation of sampled analog signals
type of PCM in which the quantization levels are linearly uniform. This is in contrast to PCM encodings in which quantization levels vary as a function
Pulse-code_modulation
Technique for the generative modeling of a continuous probability distribution
Fang; Zhang, Bo; Chen, Dongdong; Yuan, Lu; Guo, Baining (2021). "Vector Quantized Diffusion Model for Text-to-Image Synthesis". arXiv:2111.14822 [cs.CV]
Diffusion_model
Secure speech system
"firsts"; this list is taken from (Bennett, 1983): The first realization of enciphered telephony The first quantized speech transmission The first transmission
SIGSALY
brackets generated. First- and second-class constraints were introduced by Dirac (1950, p. 136, 1964, p. 17) as a way of quantizing mechanical systems
First-class_constraint
Mathematics award
with the first-ever IMU silver plaque in recognition of his proof of Fermat's Last Theorem. Don Zagier referred to the plaque as a "quantized Fields Medal"
Fields_Medal
Elementary particle or quantum of light
energy quantization resulted from some unknown constraint on the matter that absorbs or emits the radiation. In 1905, Einstein was the first to propose
Photon
Physical hypothesis
Redshift quantization, also referred to as redshift periodicity, redshift discretization, preferred redshifts and redshift-magnitude bands, is the hypothesis
Redshift_quantization
Open source amateur radio mode
US-based company Connect Systems, Inc. released the CS7000-M17, being the first commercial off-the-shelf handheld transceiver with native M17 support. Links
M17_(amateur_radio)
Asymmetry of classical and quantum action
conserved as a classical symmetry of electrodynamics, but is broken by the quantized theory. The relationship of this anomaly to the Atiyah–Singer index theorem
Anomaly_(physics)
Subatomic particle with positive charge
organic) molecules by nuclear magnetic resonance. This method uses the quantized spin magnetic moment of the proton, which is due to its angular momentum
Proton
experiment: quantization should not have been observable. At least five years would elapse before this mystery was resolved: quantization was observed
History_of_quantum_mechanics
Russian mathematician and physicist (1934–2017)
three-body problem and for the development of path-integral methods in the quantization of non-abelian gauge field theories, including the introduction of the
Ludvig_Faddeev
The quantized state systems (QSS) methods are a family of numerical integration solvers based on the idea of state quantization, dual to the traditional
Quantized state systems method
Quantized_state_systems_method
also be "water". Hence, the predicate "apple" is quantized, while "water" is not. Formally, a quantization predicate QUA can be defined as follows, where
Quantization_(linguistics)
Mathematical statistics distance measure
using Kullback–Leibler divergences between the two distributions in a quantized embedding space of a foundation model. Many of the other quantities of
Kullback–Leibler_divergence
Video or display resolutions with a width of around 4,000 pixels
characteristics as defined in the standard, including color primaries, quantization parameters, and the electro-optical transfer function. These are the
4K_resolution
Description of gravity using discrete values
Carlo Rovelli and Lee Smolin to derive naturally from a non-perturbative quantization of general relativity. Spin networks do not represent quantum states
Quantum_gravity
Quasiparticle of mechanical vibrations
mechanical quantization of the modes of vibrations for elastic structures of interacting particles. Phonons can be thought of as quantized sound waves
Phonon
Telecommunications and signal processing technique
limited-range uniform quantizer, and a (continuous-domain) signal dynamic range expander that inverts the compressor function. This type of quantization is frequently
Companding
Classical theory of gravitation
(McGraw-Hill). Petti, R. J. (1976). "Some aspects of the geometry of first-quantized theories". General Relativity and Gravitation. 7 (11): 869–883. Bibcode:1976GReGr
Einstein–Cartan_theory
Theory of subatomic structure
Friedan, Emil Martinec and Stephen Shenker further developed the covariant quantization of the superstring using conformal field theory techniques. David Gross
String_theory
British physicist (1902–1984)
quantisation of curved spacetime. He also published a paper entitled "Quantization of the Gravitational Field" in the 1967 ICTP/IAEA Trieste Symposium on
Paul_Dirac
Amateur radio communications software
compound callsign and/or 6 digit locator use a two-transmission sequence. The first transmission carries compound callsign and power level, or standard callsign
WSPR_(amateur_radio_software)
Distortion of media caused by lossy data compression
after reconstruction. Because this quantization process is applied individually in each block, neighboring blocks quantize coefficients differently. This
Compression_artifact
GPU microarchitecture designed by Nvidia
architecture introduced the Transformer Engine, software to facilitate quantization of higher-precision models (e.g., FP32) to lower precision, for which
Blackwell_(microarchitecture)
Chemical element with atomic number 1 (H)
According to quantum theory, this behavior arises from the spacing of the (quantized) rotational energy levels, which are particularly wide-spaced in H2 because
Hydrogen
Description of physical properties at the atomic and subatomic scale
of quantum field theory, which applies quantization to a field (rather than a fixed set of particles). The first complete quantum field theory, quantum
Quantum_mechanics
Digital audiovisual data interface
CEA-861-E document defines "video formats and waveforms; colorimetry and quantization; transport of compressed and uncompressed LPCM audio; carriage of auxiliary
HDMI
Quantum field theory with four-point interactions
_{\mu }\varphi -m^{2}\varphi ^{2}]-{\frac {\lambda }{4!}}\varphi ^{4}.} The first term between the brackets is the energy related to the four-momentum of
Quartic_interaction
Flaws caused by insufficient color depth
time stretching, which adds frames. Downsampling Quantization error Discretization error Color quantization Level-set method Chao, Cheng-Kang Ted (15 July
Posterization
Teleprinter commonly used 1930s–1980s
where voice or other teledata would be unintelligible. The device was first developed in the late 1920s, and saw use starting in the 1930s, chiefly
Hellschreiber
Average uncertainty in variable's states
distribution is to describe than a distribution that is uniform over its quantization scheme. Another useful measure of entropy that works equally well in
Entropy_(information_theory)
Propagation of information or matter faster than the speed of light
this property are called tachyons or tachyonic particles. Attempts to quantize them failed to produce faster-than-light particles, and instead illustrated
Faster-than-light
Branch of mathematics
rings and graded algebras; and constructions related to deformation quantization, groupoid C*-algebras, cyclic homology, and K-theory. A standard example
Noncommutative_geometry
IEEE standard for floating-point arithmetic
signaled if any non-zero digits are discarded. Additionally, operations like quantize when either operand is infinite, or when the result does not fit the destination
IEEE_754
Large language model by Meta AI
both tensors and metadata. The format focuses on supporting different quantization types, which can reduce memory usage, and increase speed at the expense
Llama_(language_model)
Large language model developed by Google
Gemini Pro was said to have outperformed GPT-3.5. Gemini Ultra was also the first language model to outperform human experts on the 57-subject Massive Multitask
Gemini_(language_model)
Spectral density of light emitted by a black body
did not propose that light propagating in free space is quantized. The idea of quantization of the free electromagnetic field was developed later, and
Planck's_law
First-order fluid First-order transition First Step to Nobel Prize in Physics First class constraint First law of thermodynamics First quantization First
Index_of_physics_articles_(F)
System for transmitting text messages
message twice to gain reliability. If the receiver detects an error in the first character, it uses the copy. If both characters are garbled, the receiver
SITOR
Special collection of states in closed string theory
configuration of sectors in orbifold conformal field theories. In the first quantized formalism of string theory (or in two-dimensional conformal field theory)
Twisted_sector
Video encoding standard
absence of any quantization and rounding errors). In reality, there are some (sometimes large) rounding errors introduced both by quantization in the encoder
MPEG-1
Quantization error in numerical analysis
arises from finite resolution in the domain, should not be confused with quantization error, which is finite resolution in the range (values), nor in round-off
Discretization_error
Light-conducting fiber
electronic level, it depends on whether the electron orbitals are spaced (or "quantized") such that they can absorb a quantum of light (or photon) of a specific
Optical_fiber
Electromagnetic effect in physics
resistance was exactly quantized. For this finding, von Klitzing was awarded the 1985 Nobel Prize in Physics. A link between exact quantization and gauge invariance
Quantum_Hall_effect
FIRST QUANTIZATION
FIRST QUANTIZATION
Girl/Female
Hindu, Indian
First
Biblical
first begotten; first fruits
Girl/Female
Hindu, Indian
First
Boy/Male
Indian
First
Boy/Male
English
From the Thicket of Trees
Girl/Female
Tamil
First
Boy/Male
Hindu, Indian
First
Boy/Male
Czechoslovakian
First.
Girl/Female
Indian, Punjabi, Sikh
First
Girl/Female
British, English
First; Always First
Girl/Female
Hindu
First
Boy/Male
Muslim
First
Boy/Male
Tamil
First
Girl/Female
Indian
First
Boy/Male
Tamil
First
Girl/Female
Biblical
First-born, first fruits.
Boy/Male
Hindu, Indian
First
Girl/Female
Indian, Sanskrit
First
Girl/Female
Hawaiian, Hebrew, Hindu, Indian, Tamil
First
Girl/Female
Latin
First.
FIRST QUANTIZATION
FIRST QUANTIZATION
Girl/Female
Arabic, Muslim
Cheering
Male
English
(×ֱלְיָסָף) Anglicized form of Hebrew Elyacaph, ELYASAF means "God increases the family." In the bible, this is the name of a leader of the tribe of Gad.
Girl/Female
Tamil
New
Girl/Female
Indian
Diamond
Girl/Female
Tamil
Girl/Female
Muslim
Happiness
Boy/Male
Indian
Energetic, Dynamic, Lively, Active
Male
African
seemed destined to die at birth.
Girl/Female
Indian, Telugu
Beautiful
Boy/Male
Indian, Telugu
Great Poet
FIRST QUANTIZATION
FIRST QUANTIZATION
FIRST QUANTIZATION
FIRST QUANTIZATION
FIRST QUANTIZATION
v. t.
To strike with the fist.
a.
First.
adv.
Before any other person or thing in time, space, rank, etc.; -- much used in composition with adjectives and participles.
adv.
Beforehand; first.
a.
Most eminent or exalted; most excellent; chief; highest; as, Demosthenes was the first orator of Greece.
a.
Obtained directly from the first or original source; hence, without the intervention of an agent.
a.
Preceding all others of a series or kind; the ordinal of one; earliest; as, the first day of a month; the first year of a reign.
a.
First; chief.
a.
Of the best class; of the highest rank; in the first division; of the best quality; first-rate; as, a first-class telescope.
a.
Foremost; in front of, or in advance of, all others.
n.
First opening or expansion; first appearance; beginning; rise.
n.
The upper part of a duet, trio, etc., either vocal or instrumental; -- so called because it generally expresses the air, and has a preeminence in the combined effect.
n. pl.
First fruits.
n.
A first game; first plan.
v. t.
To gripe with the fist.
adv.
In the first place; first in order.
a.
First-formed.
adv.
First.