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Approximation or recovery of classical mechanics in certain theories
The classical limit or correspondence limit is the ability of a physical theory to approximate or "recover" classical mechanics when considered over special
Classical_limit
Category of theories
Classical physics consists of scientific theories in the field of physics that are non-quantum or both non-quantum and non-relativistic, depending on
Classical_physics
Theory of interwoven space and time by Albert Einstein
be able to reach more than the few solar systems that exist within the limit of 100 light years from Earth. However, because of time dilation, a hypothetical
Special_relativity
Wigner distribution function in physics as opposed to in signal processing
to compact regions larger than a few ħ, and hence disappear in the classical limit. They are shielded by the uncertainty principle, which does not allow
Wigner quasiprobability distribution
Wigner_quasiprobability_distribution
Limit on measurements at quantum scales
limit. Note that due to an overloading of the word "limit", the classical limit is not the opposite of the quantum limit. In "quantum limit", "limit"
Quantum_limit
Physics principle formulated by Niels Bohr
reproduces classical physics in the limit of large quantum numbers: for large orbits and for large energies, quantum calculations must agree with classical calculations
Correspondence_principle
Conceptual parallel between optics and classical mechanics
configuration space for a multi-particle system. Albert Messiah considers a classical limit of the Schrödinger equation. He finds there an optical analogy. The
Hamilton's optical-mechanical analogy
Hamilton's_optical-mechanical_analogy
Electron-many photon scattering
some seminal works had emerged dealing with the description of the classical limit of NICS, called non-linear Thomson scattering or multiphoton Thomson
Non-linear inverse Compton scattering
Non-linear_inverse_Compton_scattering
Formulation of quantum mechanics
the stationary action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum
Path_integral_formulation
Equations describing classical electromagnetism
exact description of electromagnetic phenomena, but are instead a classical limit of the more precise theory of quantum electrodynamics. The two most
Maxwell's_equations
Short "burst" or "envelope" of restricted wave action that travels as a unit
atomic and subatomic systems using Schrödinger's wave equation. The classical limit of quantum mechanics and many formulations of quantum scattering use
Wave_packet
Physics developed since 1900
Fermi–Dirac or Bose–Einstein distributions have to be used instead. The classical limit of a modern model is a simplified model created by analyzing the modern
Modern_physics
Fundamental theorem in probability theory and statistics
{\displaystyle \mu } as n → ∞ . {\displaystyle n\to \infty .} The classical central limit theorem describes the size and the distributional form of the stochastic
Central_limit_theorem
quantization roughly amounts to finding a (quantum) algebra whose classical limit is a given (classical) algebra such as a Lie algebra or a Poisson algebra. Intuitively
Deformation_quantization
Integrable classical system
'Painlevé simplification' or 'autonomous limit' of the Schlesinger equations. It may be interpreted as the classical limit of the quantum Gaudin model due to
Garnier_integrable_system
System in quantum mechanics
quantum-mechanical result we will return to the question of how to recover the classical limit. To study the quantum case, consider the following situation: a particle
Step_potential
Hypothetical gravitational object composed of matter
the (super) classical limit of quantum electrodynamics, and for the Einstein–Yang–Mills–Dirac system, which is the (super) classical limit of the standard
Black star (semiclassical gravity)
Black_star_(semiclassical_gravity)
Fundamental mechanical principles
classical physics, phases tend to align; the tendency is stronger for more massive objects that have larger values of action. In the classical limit,
Action_principles
Branch of physics seeking to explain chaotic dynamical systems in terms of quantum theory
classical chaos?" The correspondence principle states that classical mechanics is the classical limit of quantum mechanics, specifically in the limit
Quantum_chaos
making connections between the quantum system under study and the classical limit. Consider the example of a simple harmonic oscillator initially at
Classical_probability_density
Scientific law that a closed system's mass remains constant
conserved. The conservation of mass is a law that holds only in the classical limit. For example, the overlap of the electron and positron wave functions
Conservation_of_mass
Theory of quantum gravity merging quantum mechanics and general relativity
the definition of a family of transition amplitudes, which in the classical limit can be shown to be related to a family of truncations of general relativity
Loop_quantum_gravity
Age of the ancient Greeks and Romans
Classical antiquity, also known as the classical era, classical period, classical age, or simply antiquity, is the period of cultural European history
Classical_antiquity
Formulation of quantum mechanics
between quantum mechanics and classical statistical mechanics, enabling a natural comparison between the two (see classical limit). Quantum mechanics in phase
Phase-space_formulation
Type of integrable system
certain limit of the Schlesinger equations, and Garnier solved his system by defining spectral curves. (The Garnier system is the classical limit of the
Hitchin_system
Concept in physics and mathematics
Poincaré transformations; conversely, the group contraction in the classical limit c → ∞ of Poincaré transformations yields Galilean transformations.
Galilean_transformation
State of matter
understood as a model input to classical theory, obtained either from a fit to experimental data or from the classical limit of a quantum mechanical description
Liquid
Interpretation of quantum mechanics
on particle positions and trajectories like classical mechanics but the dynamics are different. In classical mechanics, the accelerations of the particles
De_Broglie–Bohm_theory
Relation satisfied by conjugate variables in quantum mechanics
}}[{\hat {H}},{\hat {P}}]\,\,.} In order for that to reconcile in the classical limit with Hamilton's equations of motion, [ H ^ , Q ^ ] {\displaystyle [{\hat
Canonical commutation relation
Canonical_commutation_relation
Approximation applicable to physical systems
particle in a gravitational potential ϕ ( x ) {\displaystyle \phi (x)} Classical limit Carroll, Sean M (1997). "Lecture Notes on General Relativity". arXiv:gr-qc/9712019
Newtonian_limit
Basic unit of quantum information
positive X-axis. In the classical limit, a qubit, which can have quantum states anywhere on the Bloch sphere, reduces to the classical bit, which can be found
Qubit
Construct in theoretical physics
to quantum commutators) to the Poisson bracket Lie algebra, in the classical limit as the Planck constant vanishes: ħ → 0. Inönü & Wigner 1953 Segal 1951
Group_contraction
Nonlinear form of the Schrödinger equation
of the classical nonlinear Schrödinger field, which in turn is a classical limit of a quantum Schrödinger field. Conversely, when the classical Schrödinger
Nonlinear Schrödinger equation
Nonlinear_Schrödinger_equation
Mathematical tool in quantum physics
function is then analogous to that of its classical limit, the Liouville equation of classical physics. In the limit of a vanishing Planck constant ℏ {\displaystyle
Density_matrix
Aspect of learning procedure
Classical conditioning (also respondent conditioning and Pavlovian conditioning) is a behavioral procedure in which a biologically potent stimulus (e
Classical_conditioning
Physical constant providing length scale to interatomic interactions
considered point charges in modern theories. The classical electron radius appears in the classical limit of modern theories as well, including non-relativistic
Classical_electron_radius
Mathematical structures that allow quantum mechanics to be explained
so-called classical limit of quantum mechanics. Also, as Bohr emphasized, human cognitive abilities and language are inextricably linked to the classical realm
Mathematical formulation of quantum mechanics
Mathematical_formulation_of_quantum_mechanics
Concept in physics and chemistry
x_{1},\,x_{2}} are the two classical turning points for the potential barrier.[failed verification] In the classical limit of all other physical parameters
Transmission_coefficient
Hypothetical elementary particle that mediates gravity
accurately described by the Standard Model of particle physics. In the classical limit, a successful theory of gravitons would reduce to general relativity
Graviton
Mathematical function, used to describe magnetization
could be seen here: The Langevin function can also be derived as the classical limit of the Brillouin function, if the magnetic moments can be continuously
Brillouin and Langevin functions
Brillouin_and_Langevin_functions
Bounds of a sequence
limits is invariant. Limit inferior is also called infimum limit, limit infimum, liminf, inferior limit, lower limit, or inner limit; limit superior is also
Limit inferior and limit superior
Limit_inferior_and_limit_superior
Physical fields obeying the Schrödinger equation
number changes. A Schrödinger field is also the classical limit of a quantum Schrödinger field, a classical wave which satisfies the Schrödinger equation
Schrödinger_field
Formulation of classical mechanics in terms of Hilbert spaces
Wigner function approaches, in the classical limit, the time evolution of the classical wavefunction of a classical particle. However, a mathematical resemblance
Koopman–von Neumann classical mechanics
Koopman–von_Neumann_classical_mechanics
Model of quantum optics
P)} . A classical Hamiltonian is obtained by taking the expectation value of the Dicke Hamiltonian given by Eq. 2 under these states, In the limit of N →
Dicke_model
to classical calculus, which is based on the narrower concept of functions. Given a sequence of distributions f i {\displaystyle f_{i}} , its limit f {\displaystyle
Limit_of_distributions
Use of both classical and quantum physics to analyze a system
also the first to write that quantum theory should replicate classical mechanics at some limit, particularly if Planck's constant h {\displaystyle h} were
Semiclassical_physics
Formulation of quantum mechanics
Xnm , and demanded that it should reduce to the classical Fourier coefficients in the classical limit. For large values of n and m but with n − m
Matrix_mechanics
Low energy photon scattering off charged particles
radiation by a free charged particle, as described by classical electromagnetism. It is the low-energy limit of Compton scattering: the particle's kinetic energy
Thomson_scattering
Interpretation of quantum mechanics
"observed" apply to any arbitrary system, microscopic or macroscopic. The classical limit is a consequence of aggregate systems of very highly correlated subsystems
Relational_quantum_mechanics
Two-dimensional conformal field theory
only if c ∈ ( 1 , + ∞ ) , {\displaystyle c\in (1,+\infty ),} and its classical limit is c → + ∞ . {\displaystyle c\to +\infty .} Although it is an interacting
Liouville_field_theory
depends on temperature, high temperatures will put most systems in the classical limit unless they have a very high density e.g. a White dwarf. For an ideal
Quantum_concentration
Quantum mechanical phenomenon
\hbar ^{-1}} to satisfy the real part of the equation; for a good classical limit starting with the highest power of the Planck constant possible is
Quantum_tunnelling
Value for the flow of probability in quantum mechanics
and v is its velocity (also the group velocity of the wave). In the classical limit, we can associate the velocity with ∇ S m , {\displaystyle {\tfrac
Probability_current
Orbital radius at which a satellite might break up due to gravitational force
and Reedy Creek Observatory. The classical Roche limit assumes that particles will generally accrete beyond this limit as satellites, large spherical bodies
Roche_limit
American mathematician
nonrelativistic quantum mechanics in electric and magnetic fields, the semi-classical limit, the singular continuous spectrum, random and ergodic Schrödinger operators
Barry_Simon
Textbook by Ramamurti Shankar
Experiment Some Theorems The Classical Limit The Harmonic Oscillator Why Study the Harmonic Oscillator? Review of the Classical Oscillator Quantization of
Principles of Quantum Mechanics
Principles_of_Quantum_Mechanics
General relativity in M-theory
treated independently. This maximal supergravity is the classical limit of M-theory. Classically, we have only one 11-dimensional supergravity theory: 7D
Higher-dimensional supergravity
Higher-dimensional_supergravity
Probability distribution
x\geq 0} . The cumulative Logistic distribution is recovered in the classical limit κ → 0 {\displaystyle \kappa \rightarrow 0} . The survival distribution
Kaniadakis logistic distribution
Kaniadakis_logistic_distribution
Formulation of general relativity
constraints fully determines the classical theory – this is something that must in some way be reproduced in the semi-classical limit of canonical quantum gravity
Canonical_quantum_gravity
Attraction of masses and energy
virtual gravitons. This description reproduces general relativity in the classical limit. However, this approach fails at short distances of the order of the
Gravity
Inequality in mathematical physics
The Lieb–Thirring inequalities can be compared to the semi-classical limit. The classical phase space consists of pairs ( p , x ) ∈ R 2 n . {\displaystyle
Lieb–Thirring_inequality
Process by which a quantum system takes on a definitive state
important for explaining the classical limit of quantum mechanics, but cannot explain wave function collapse, as all classical alternatives are still present
Wave_function_collapse
Swedish mathematician
Astérisque 95, 1982 with Bernard Helffer: Multiple wells in the semi-classical limit, Part 1, Communications in PDE, 9, 1984, 337–408 (6 parts altogether
Johannes_Sjöstrand
Physical quantity of hot and cold
a special case of the equipartition theorem, and holds only in the classical limit of a perfect gas. It does not hold exactly for most substances. When
Temperature
Repetitive variation of some measure about a central value
string or the surface of a body of water. Such systems have (in the classical limit) an infinite number of normal modes and their oscillations occur in
Oscillation
of quantum operators can be expressed. In the classical limit, quantum characteristics reduce to classical trajectories. The knowledge of quantum characteristics
Method of quantum characteristics
Method_of_quantum_characteristics
Mathematical theorem about the real analytic Eisenstein series
In mathematics, the classical Kronecker limit formula describes the constant term at s = 1 of a real analytic Eisenstein series (or Epstein zeta function)
Kronecker_limit_formula
Aspect of astrophysics history
on the semi-classical limit, the continuum limit, and dynamics was intense after this, but progress was slower. On the semi-classical limit front, the
History of loop quantum gravity
History_of_loop_quantum_gravity
Statistical physics approach
y)\,\right)} , where the ordinary sum is a particular case in the classical limit κ → 0 {\displaystyle \kappa \rightarrow 0} : x ⊕ 0 y = x + y {\displaystyle
Kaniadakis_statistics
systems (ergodic with a classical limit) few degrees of freedom holds that spectra of time reversal-invariant systems whose classical analogues are K-systems
BGS_conjecture
Expansion coefficients in statistical mechanics
{\displaystyle Q_{1}} contains only a kinetic energy term. In the classical limit ℏ = 0 {\displaystyle \hbar =0} the kinetic energy operators commute
Virial_coefficient
Heat required to raise the temperature of a given unit of mass of a substance
in a gas. The Dulong–Petit limit results from the equipartition theorem, and as such is only valid in the classical limit of a microstate continuum, which
Specific_heat_capacity
Quantum
(11 November 2011). "Twin Matter Waves for Interferometry Beyond the Classical Limit". Science. 334 (6057): 773–776. arXiv:1204.4102. Bibcode:2011Sci..
Quantum_Fisher_information
Property of a thermodynamic system
because in the classical limit, when the phases between the basis states are purely random, this expression is equivalent to the familiar classical definition
Entropy
Potential for two waves to interfere
creation of uniquely quantum coherence analysis. Classical optical coherence becomes a classical limit for first-order quantum coherence; higher degree
Coherence_(physics)
Measure of relative information in quantum information theory
coherent information, and gives the additional number of bits above the classical limit that can be transmitted in a quantum dense coding protocol. Positive
Conditional_quantum_entropy
Description of the ground state of a quantum system
semi-classical limit of the many body theory of s-wave interacting identical bosons represented in terms of coherent states. The semi-classical limit is
Gross–Pitaevskii_equation
Energy scale at which vacuum effects become important
electrodynamics (QED), the Schwinger limit is a scale above which the electromagnetic field is expected to become nonlinear. The limit was first derived in one of
Schwinger_limit
Gauge boson self-energy due to interactions with virtual particles
Maxwell's equations are the classical limit of the quantum electrodynamics which cannot be described by any classical theory. A point charge must be
Vacuum_polarization
Any technique to improve resolution of an imaging system beyond conventional limits
Lukosz, W., 1966. Optical systems with resolving power exceeding the classical limit. J. opt. soc. Am. 56, 1463–1472. Guerra, John M. (1995-06-26). "Super-resolution
Super-resolution_imaging
Relativistic quantum mechanical wave equation
populating the field with a sufficient number of particles to reach the classical limit. The Lorentz group SO ( 1 , 3 ) {\displaystyle {\text{SO}}(1,3)} ,
Dirac_equation
Specific microscopic configuration of a thermodynamic system
the quantum case find no analogous definition in the classical limit. The reason is that classical microstates are not defined in relation to a precise
Microstate (statistical mechanics)
Microstate_(statistical_mechanics)
Concept in statistical physics
between spins. The classical Heisenberg model is the semiclassical limit of the isotropic spin-s quantum Heisenberg model in the limit as s becomes large
Classical_Heisenberg_model
Hydrodynamic formulation of the Schrödinger equations
related to the von Weizsäcker correction of density functional theory. Classical limit De Broglie–Bohm theory Magnetohydrodynamics Pilot wave theory Quantum
Madelung_equations
Formulation of quantum mechanics
[H,[H,A]]]+\cdots } A similar relation also holds for classical mechanics, the classical limit of the above, given by the correspondence between Poisson
Heisenberg_picture
Formulation of classical mechanics
} This is the Schrödinger equation in nonlinear Riccati form. The classical limit ( ℏ → 0 {\displaystyle \hbar \rightarrow 0} ) of the Schrödinger equation
Hamilton–Jacobi_equation
Suitably normalized antisymmetrization of the phase-space star product
bracket equals the ordinary product up to higher orders of ħ. In the classical limit, the Moyal bracket helps reduction to the Liouville equation (formulated
Moyal_bracket
Continuous probability distribution
x\geq 0} . The cumulative Weibull distribution is recovered in the classical limit κ → 0 {\displaystyle \kappa \rightarrow 0} . The survival distribution
Kaniadakis Weibull distribution
Kaniadakis_Weibull_distribution
Mathematical tool from spectral theory and functional analysis
Dimassi, M.; Sjostrand, J. (1999). Spectral Asymptotics in the Semi-Classical Limit. London Mathematical Society Lecture Note Series. Cambridge: Cambridge
Helffer–Sjöstrand_formula
Dispersionless (or quasi-classical) limits of integrable partial differential equations (PDE) arise in various problems of mathematics and physics and
Dispersionless_equation
Limitation on the minimum time for a quantum system to evolve between two states
In quantum mechanics, a quantum speed limit (QSL) is a limitation on the minimum time for a quantum system to evolve between two distinguishable (orthogonal)
Quantum_speed_limit
Linearized quantum-mechanical equation
Poincaré group to explain some properties of spin 1/2 systems. In the classical limit where c → ∞ {\textstyle c\to \infty } , quantum mechanics under the
Lévy-Leblond_equation
Measure of nonclassical correlations between two subsystems of a quantum system
discord is the difference between two expressions which each, in the classical limit, represent the mutual information. These two expressions are: I ( A
Quantum_discord
Quantization giving rise to photons
role. The waves emitted by this station are well-described by the classical limit and quantum mechanics is not needed. QED vacuum Generalized polarization
Quantization of the electromagnetic field
Quantization_of_the_electromagnetic_field
Arithmetic operation
analogy with the Planck constant from quantum mechanics, and taking the "classical limit" as h {\displaystyle h} tends to zero: max ( a , b ) = lim h → 0 h
Addition
Astrophysical limit on radiation from stars
when calculating this limit, something that now is called the classical Eddington limit. Nowadays, the modified Eddington limit also takes into account
Eddington_luminosity
Model of a quantum/optical system
the operators are uncorrelated, and is a good approximation in the classical limit. It turns out that the resulting equations give the correct qualitative
Maxwell–Bloch_equations
Poisson algebras as well. This observation is important in studying the classical limit of quantum mechanics—the non-commutative algebra of operators on a
Poisson_ring
American-Brazilian-British scientist (1917–1992)
approximation in which certain criteria are fulfilled. In that picture, the classical limit for quantum phenomena, in terms of a condition that the action function
David_Bohm
Hypothesis about quantum and statistical mechanics
semi-classical limit, where the validity of the ETH rests on the validity of Shnirelman's theorem, which states that in a system which is classically chaotic
Eigenstate thermalization hypothesis
Eigenstate_thermalization_hypothesis
CLASSICAL LIMIT
CLASSICAL LIMIT
Girl/Female
Tamil
Light classical melody
Girl/Female
Indian
Raga in hindustani classical music
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Light Classical Melody
Girl/Female
Assamese, Gujarati, Hindu, Indian, Sindhi
Raga in Hindustani Classical Music
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu
A Classical Melody
Girl/Female
Tamil
A classical melody, From the east
Girl/Female
Hindu, Indian
Name of a Classical Melody
Girl/Female
Hindu, Indian
A Classical Melody
Girl/Female
Indian, Sanskrit, Traditional
A Name of Indian Classical Raga
Girl/Female
Hindu
A classical melody, From the east
Girl/Female
Hindu, Indian, Traditional
A Classical Melody
Girl/Female
Hindu
A classical melody, From the east
Boy/Male
Tamil
Bnidhish | பà¯à®¨à¯€à®¤à¯€à®·Â
Lyrics of classical music
Bnidhish | பà¯à®¨à¯€à®¤à¯€à®·Â
Boy/Male
Tamil
The th not of classical music
Boy/Male
Hindu, Indian
Lyrics of Classical Music
Girl/Female
Tamil
A classical melody, From the east
Girl/Female
Tamil
Raga in hindustani classical music
Girl/Female
Hindu, Indian, Marathi, Tamil
A Classic
Girl/Female
Indian, Tamil
Poem; Classical Form
Boy/Male
Hindu
The th not of classical music
CLASSICAL LIMIT
CLASSICAL LIMIT
Girl/Female
Hindu
Boy/Male
Hindu, Indian, Punjabi, Sikh, Traditional
Loving and Delightful
Boy/Male
Tamil
The ear
Surname or Lastname
English
English : habitational name from any of the many places so called, from Old English norð ‘north’ + wudu ‘wood’.
Girl/Female
Muslim
Just. Honest. Equal.
Boy/Male
Hindu
Horse rider, A star
Boy/Male
Tamil
Skilled in literature
Male
Hebrew
(×—Ö²× ï‹×šÖ°) Hebrew name CHANOWK means "dedicated" or "initiated." In the bible, this is the name of the eldest son of Cain, and a son of Jared the father of Methuselah. Enoch is the Anglicized form.
Male
Italian
 Pet form of Italian Leopoldo, POLDI means "people-bold." Compare with another form of Poldi.
Girl/Female
Hindu, Indian, Marathi
Flame; Fire
CLASSICAL LIMIT
CLASSICAL LIMIT
CLASSICAL LIMIT
CLASSICAL LIMIT
CLASSICAL LIMIT
n.
Of or pertaining to the ancient Greeks and Romans, esp. to Greek or Roman authors of the highest rank, or of the period when their best literature was produced; of or pertaining to places inhabited by the ancient Greeks and Romans, or rendered famous by their deeds.
n.
One learned in the literature of Greece and Rome, or a student of classical literature.
n.
Mental cultivation; liberal education; instruction in classical and polite literature.
a.
Not classical or correct.
a.
Of or relating to algebra; as, cossic numbers, or the cossic art.
n.
Of or relating to the first class or rank, especially in literature or art.
adv.
In the manner of classes; according to a regular order of classes or sets.
n. pl.
Sculptured ornaments, used in classical architecture, representing rams' heads or skulls.
n.
One learned in the classics; an advocate for the classics.
n.
A concave molding; -- used chiefly in classical architecture. See Illust. of Column.
n.
The quality of being classical.
n.
An American bird of the genus Cassicus, allied to the starlings and orioles, remarkable for its skillfully constructed and suspended nest; the crested oriole. The name is also sometimes given to the piping crow, an Australian bird.
n.
A classical idiom, style, or expression; a classicism.
a.
Elastic.
n.
A concave molding used especially in classical architecture.
n.
Conforming to the best authority in literature and art; chaste; pure; refined; as, a classical style.
a.
Alt. of Cossical
adv.
In a classical manner; according to the manner of classical authors.
n.
Alt. of Classical
a.
See Plastic.