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Function acting on the space of physical states in physics
An operator is a function over a space of physical states onto another space of states. The simplest example of the utility of operators is the study
Operator_(physics)
Function acting on function spaces
(see Operator (physics) for other examples) The most basic operators are linear maps, which act on vector spaces. Linear operators refer to linear maps
Operator_(mathematics)
Quantum operator for the sum of energies of a system
quantum physics. Similar to vector notation, it is typically denoted by H ^ {\displaystyle {\hat {H}}} , where the hat indicates that it is an operator. It
Hamiltonian (quantum mechanics)
Hamiltonian_(quantum_mechanics)
First-order differential linear operator on spinor bundle, whose square is the Laplacian
applications to analytical physics must be extensive in a high degree. D = − i ∂ x {\displaystyle D=-i\partial _{x}} is a Dirac operator on the tangent bundle
Dirac_operator
Topics referred to by the same term
wh- interrogatives Operator (physics), mathematical operators in quantum physics Operator (band), an American hard rock band Operators, a synth pop band
Operator
mechanics List of equations in nuclear and particle physics List of equations Operator (physics) Laws of science Physical constant Physical quantity
Lists_of_physics_equations
Description of a quantum-mechanical system
evolution generated by a Hamiltonian operator, as in the Schrödinger functional method. Attempts to combine quantum physics with special relativity began with
Schrödinger_equation
Conjugate transpose of an operator in infinite dimensions
fields like physics, especially when used in conjunction with bra–ket notation in quantum mechanics. In finite dimensions where operators can be represented
Hermitian_adjoint
Description of physical properties at the atomic and subatomic scale
Quantum mechanics, also known as quantum physics, is the fundamental physical theory that describes the behavior of matter and of light; its unusual characteristics
Quantum_mechanics
Differential operator used in vector calculus
seen above in the case of the Laplacian. del d'Alembert operator "12.2: Vector Operators". Physics LibreTexts. 2020-05-09. Retrieved 2025-05-14. H. M. Schey
Vector_operator
Any entity that can be measured
In physics, an observable is a physical property or physical quantity that can be measured. In classical mechanics, an observable is a real-valued "function"
Observable
Operators useful in quantum mechanics
is the adjoint of the annihilation operator. In many subfields of physics and chemistry, the use of these operators instead of wavefunctions is known as
Creation and annihilation operators
Creation_and_annihilation_operators
Machine learning framework
paradigm to operator learning are broadly called physics-informed neural operators (PINO), where loss functions can include full physics equations or
Neural_operators
Branch of applied mathematics
Mathematical physics is the development of mathematical methods for use in physics and their applications. A broader definition would include the development
Mathematical_physics
Projection of spin along the direction of momentum
In physics, helicity is the projection of the spin onto the direction of momentum. Mathematically, helicity is the sign of the projection of the spin
Helicity_(particle_physics)
Mathematical conjecture about the Riemann zeta function
Physics A: Mathematical and Theoretical, 43 (9): 37, arXiv:0912.3183v5, doi:10.1088/1751-8113/43/9/095204, S2CID 115162684 Simon, B. (2015), Operator
Hilbert–Pólya_conjecture
Operator in quantum mechanics
quantum mechanics, the momentum operator is the operator associated with the linear momentum. The momentum operator is, in the position representation
Momentum_operator
Broad concept generalizing scalars in mathematics and physics
In mathematics and physics, a vector is a generalization of a single number. It may denote a vector quantity, i.e., physical quantity that cannot be expressed
Vector (mathematics and physics)
Vector_(mathematics_and_physics)
Differential operator in mathematics
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean
Laplace_operator
unsolved problems grouped into broad areas of physics. Some of the major unsolved problems in physics are theoretical, meaning that existing theories
List of unsolved problems in physics
List_of_unsolved_problems_in_physics
Linear operator equal to its own adjoint
operator is almost as good as having a self-adjoint operator, since we merely need to take the closure to obtain a self-adjoint operator. In physics,
Self-adjoint_operator
Specific quantum state of a quantum harmonic oscillator
ff L. Susskind and J. Glogower, Quantum mechanical phase and time operator,Physics 1 (1963) 49. Carruthers, P.; Nieto, Michael Martin (1968-04-01). "Phase
Coherent_state
Symmetry of spatially mirrored systems
In physics, a parity transformation (also called parity inversion) is the flip in the sign of one spatial coordinate. In three dimensions, it can also
Parity_(physics)
Quantum mechanical operator related to rotational symmetry
angular momentum operator is one of several related operators analogous to classical angular momentum. The angular momentum operator plays a central role
Angular_momentum_operator
Low energy theories not compatible with string theory
In physics, the term swampland refers to effective low-energy physical theories which are not compatible with quantum gravity. This is in contrast with
Swampland_(physics)
Intrinsic quantum property of particles
Hamiltonian to its conjugate momentum, which is the total angular momentum operator J = L + S . Therefore, if the Hamiltonian H has any dependence on the spin
Spin_(physics)
Analog of the continuous Laplace operator
vertices), the discrete Laplace operator is more commonly called the Laplacian matrix. The discrete Laplace operator occurs in physics problems such as the Ising
Discrete_Laplace_operator
Influence that can change motion of an object
In physics, a force is an action that can cause an object to change its velocity or its shape, or to resist other forces, or to cause changes of pressure
Force
Branch of mathematics
They are central in Connes' operator-algebraic formulation of noncommutative geometry and in applications to particle physics and index theory. Differential
Noncommutative_geometry
Systematic procedure of turning a classical theory into a quantum one
procedure is basic to theories of atomic physics, chemistry, particle physics, nuclear physics, condensed matter physics, and quantum optics. In 1901, when
Quantization_(physics)
Physics phenomenon
entanglement is at the heart of the disparity between classical physics and quantum physics: entanglement is a primary feature of quantum mechanics not present
Quantum_entanglement
Physical quantity
the conservation of energy is a consequence of the fact that the laws of physics do not change over time. Thus, since 1918, theorists have understood that
Energy
Bijective antilinear map between two complex Hilbert spaces
Antiunitary Symmetry Operators", Journal of Mathematical Physics Vol 1, no 5, 1960, pp.414–416 Unitary operator Wigner's Theorem Particle physics and representation
Antiunitary_operator
Symbol used to indicate the del operator
in which the mathematics of the operator in question is now usually expressed—most notably in undergraduate physics, and especially electrodynamics,
Nabla_symbol
Method of statistical physics
statistical physics. It allows the splitting of the dynamics of a system into a relevant and an irrelevant part using projection operators, which helps
Mori–Zwanzig_formalism
Profession that involves the operation of specific equipment or service
computing, power generation and transmission, customer service, physics, and construction. Operators are day-to-day end users of systems, that may or may not
Operator_(profession)
Generalized function whose value is zero everywhere except at zero
Mathematical Physics, Volume II, Wiley-Interscience. Davis, Howard Ted; Thomson, Kendall T (2000), Linear algebra and linear operators in engineering
Dirac_delta_function
International System of Units ISO 31 Elert, Glenn. "Special Symbols". The Physics Hypertextbook. Retrieved 4 August 2021. NIST (16 August 2023). "SI Units"
List of common physics notations
List_of_common_physics_notations
Branch of functional analysis
functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication
Operator_algebra
Formulation to quantize gauge field theories in physics
"Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism", Lebedev Physics Institute preprint 39 (1975), arXiv:0812.0580. Kugo
BRST_quantization
In physics, a linear operator acting on a vector space of linear operators
In physics, a superoperator is a linear operator acting on a vector space of linear operators. Sometimes the term refers more specially to a completely
Superoperator
Mathematical function, in linear algebra
of all functions. It also defines a linear operator on the space of all smooth functions (a linear operator is a linear endomorphism, that is, a linear
Linear_map
Mathematical structures that allow quantum mechanics to be explained
of operators representing quantum observables. Prior to the development of quantum mechanics as a separate theory, the mathematics used in physics consisted
Mathematical formulation of quantum mechanics
Mathematical_formulation_of_quantum_mechanics
Operator in quantum physics
In quantum physics, the squeeze operator for a single mode of the electromagnetic field is S ^ ( z ) = exp ( 1 2 ( z ∗ a ^ 2 − z a ^ † 2 ) ) , z = r
Squeeze_operator
Fact that observing a situation changes it
In physics, the observer effect is the disturbance of a system by the act of observation. This is often the result of utilising instruments that, by necessity
Observer_effect_(physics)
Method for approximating many-body systems
in the field of computational chemistry, but it is also used in nuclear physics. Coupled cluster essentially takes the basic Hartree–Fock molecular orbital
Coupled_cluster
Algebraic object with geometric applications
have become important in physics, because they provide a concise mathematical framework for formulating and solving physics problems in areas such as
Tensor
Exterior algebraic map taking tensors from p forms to n-p forms
In mathematics, the Hodge star operator or Hodge star is a linear map defined on the exterior algebra of a finite-dimensional oriented vector space endowed
Hodge_star_operator
Symbols for constants, special functions
certain investments. Some common conventions: Intensive quantities in physics are usually denoted with minuscules while extensive are denoted with capital
Greek letters used in mathematics, science, and engineering
Greek_letters_used_in_mathematics,_science,_and_engineering
Differential equation important in physics
dynamics. This article focuses on waves in classical physics. Quantum physics uses an operator-based wave equation often as a relativistic wave equation
Wave_equation
Scientific subjects
physics, and molecular physics; optics and acoustics; condensed matter physics; high-energy particle physics and nuclear physics; and chaos theory and
Branches_of_physics
Array of numbers describing a metric connection
In mathematics and physics, the Christoffel symbols are an array of numbers describing a metric connection. The metric connection is a specialization
Christoffel_symbols
Branch of functional analysis
Operator Algebras: Vol 1. Amer Mathematical Society. ISBN 0-8218-0819-2. Reed, Michael; Simon, Barry (1981). Methods of Modern Mathematical Physics.
Borel_functional_calculus
Mathematical tool in quantum physics
In quantum mechanics, a density matrix (or density operator) is a matrix used in calculating the probabilities of the outcomes of measurements performed
Density_matrix
Branch of physics
Theoretical physics is a branch of physics that uses mathematical models and abstractions of physical objects and systems to explain and predict natural
Theoretical_physics
Mathematical result in differential geometry
cases, and has applications to theoretical physics. The index problem for elliptic differential operators was posed by Israel Gel'fand. He noticed the
Atiyah–Singer_index_theorem
Mathematical function of two variables; outputs 1 if they are equal, 0 otherwise
. The Kronecker delta appears naturally in many areas of mathematics, physics, engineering and computer science, as a means of compactly expressing its
Kronecker_delta
Physics of many interacting particles
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic
Statistical_mechanics
Specification of a derivative along a tangent vector of a manifold
and working with a connection on a manifold by means of a differential operator, to be contrasted with the approach given by a principal connection on
Covariant_derivative
results below come from pure mathematics, but some are from theoretical physics, economics, and other applied fields. Ax–Grothendieck theorem (model theory)
List_of_theorems
Change of state over time, especially in physics
also Fu, s(x). In some contexts in mathematical physics, the mappings Ft, s are called propagation operators or simply propagators. In classical mechanics
Time_evolution
Typically linear operator defined in terms of differentiation of functions
In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first
Differential_operator
Discrete analog of a derivative
differentiation. The difference operator, commonly denoted Δ {\displaystyle \Delta } (uppercase Delta), is the operator that maps a function f to the function
Finite_difference
In mathematics, a linear operator acting on inner product space
mathematics (specifically linear algebra, operator theory, and functional analysis) as well as physics, a linear operator A {\displaystyle A} acting on an inner
Positive_operator
Formulation of the quantum many-body problem
thought of as field operators, in a manner similar to how the physical quantities (position, momentum, etc.) are thought of as operators in first quantization
Second_quantization
Linear operator in mathematics
composition operators is covered by AMS category 47B33. In physics, and especially the area of dynamical systems, the composition operator is usually referred
Composition_operator
Methods of mathematical approximation
Hamiltonian from the very beginning and never specifies a perturbation operator as such. Møller–Plesset perturbation theory uses the difference between
Perturbation_theory
Property of a mathematical space
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify
Dimension
Raising and lowering operators in quantum mechanics
or lowering operator (collectively known as ladder operators) is an operator that increases or decreases the eigenvalue of another operator. In quantum
Ladder_operator
Fourteenth letter in the Greek alphabet
dynamics Potential difference in physics (in volts) The radial integral in the spin-orbit matrix operator in atomic physics. The Killing vector in general
Xi_(letter)
Operator shifting particles and fields by a certain amount in a certain direction
Hamiltonian, i.e. when laws of physics are translation-invariant. This is an example of Noether's theorem. The translation operator T ^ ( x ) {\displaystyle
Translation operator (quantum mechanics)
Translation_operator_(quantum_mechanics)
Vector differential operator
Del, or nabla, is an operator used in mathematics (particularly in vector calculus) as a vector differential operator, usually represented by ∇ (the nabla
Del
Quantum mechanical system that interacts with a quantum-mechanical environment
In physics, an open quantum system is a quantum mechanical system that interacts with an external quantum system, known as the environment or the bath
Open_quantum_system
Operation in mathematics
Groups. GTM. Vol. 94. New York: Springer. pp. 54–56. ISBN 0-387-90894-3. In physics (and sometimes in mathematics), indices often start with zero instead of
Tensor_contraction
Array of numbers
number theory to physics. The first model of quantum mechanics (Heisenberg, 1925) used infinite-dimensional matrices to define the operators that took over
Matrix_(mathematics)
Topics referred to by the same term
keyboard →, ->, representing the assignment operator in various programming languages ->, a pointer operator in C and C++ where a->b is synonymous with
→
Mathematical entity to describe the probability of each possible measurement on a system
In quantum physics, a quantum state is a mathematical entity that represents a physical system. Quantum mechanics specifies the construction, evolution
Quantum_state
Mathematical operation in quantum optics, general relativity and other areas of physics
In theoretical physics, the Bogoliubov transformation, also known as the Bogoliubov–Valatin transformation, was independently developed in 1958 by Nikolay
Bogoliubov_transformation
English broadcaster and natural historian (born 1926)
Science of underwater diving List of researchers in underwater diving Diving physics Metre sea water Neutral buoyancy Underwater acoustics Modulated ultrasound
David_Attenborough
Class of operators in quantum field theory
(IR) physics significantly (e.g. because the vacuum expectation value (VEV) of some field depends sensitively upon the coefficient of this operator). In
Dangerously irrelevant operator
Dangerously_irrelevant_operator
Concept relating to waves and signals
Tandem mass spectrometry is used to determine molecular structure. In physics, the energy spectrum of a particle is the number of particles or intensity
Spectrum_(physical_sciences)
Interaction of a quantum system with a classical observer
self-adjoint operator on that Hilbert space termed an "observable". These observables play the role of measurable quantities familiar from classical physics: position
Measurement in quantum mechanics
Measurement_in_quantum_mechanics
Amount of matter present in an object
Mass is an intrinsic property of a body. In modern physics, it is generally defined as the strength of an object's gravitational attraction to other bodies
Mass
Properties underlying modern physics
commutator.) One aspect of generators in theoretical physics is they can be constructed themselves as operators corresponding to symmetries, which may be written
Symmetry_in_quantum_mechanics
Covariant derivative of the metric tensor
geometry Exterior calculus Multilinear algebra Tensor algebra Tensor calculus Physics Engineering Computer vision Continuum mechanics Electromagnetism General
Nonmetricity_tensor
1932 book by John von Neumann
uniqueness of Schrödinger operators]". Mathematische Annalen. 104: 570–578. doi:10.1007/bf01457956. S2CID 120528257. Books portal Physics portal Mathematics
Mathematical Foundations of Quantum Mechanics
Mathematical_Foundations_of_Quantum_Mechanics
1945–1946 sphere of plutonium
nuclear tests scheduled a month later at Bikini Atoll. It required the operator to place two half-spherical shells of beryllium (a neutron reflector) around
Demon_core
International science award since 2012
in Fundamental Physics is one of the Breakthrough Prizes, awarded by the Breakthrough Prize Board. Initially named Fundamental Physics Prize, it was launched
Breakthrough Prize in Fundamental Physics
Breakthrough_Prize_in_Fundamental_Physics
Country in Southeast Asia
modest starting point. Publications focus mainly on life sciences (22%), physics (13%), and engineering (13%), which is consistent with recent advances
Vietnam
Millennium Prize Problem
existence and mass gap problem is an unsolved problem in mathematical physics and mathematics, and one of the seven Millennium Prize Problems defined
Yang–Mills existence and mass gap
Yang–Mills_existence_and_mass_gap
Matrices important in quantum mechanics and the study of spin
In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 {\displaystyle 2\times 2} complex matrices that are traceless, Hermitian
Pauli_matrices
Expected value of a quantum measurement
statistics. It is a fundamental concept in all areas of quantum physics. Consider an operator A {\displaystyle A} . The expectation value is then ⟨ A ⟩ =
Expectation value (quantum mechanics)
Expectation_value_(quantum_mechanics)
Branch of mathematics
In operator theory and spectral theory, the resolvent of an operator encodes information about its spectrum and often allows functions of operators to
Mathematical_analysis
Self-adjoint operator that arises in physical transition problems
In mathematical physics, the almost Mathieu operator, named for its similarity to the Mathieu operator introduced by Émile Léonard Mathieu, arises in the
Almost_Mathieu_operator
Monster and modular connection
This vertex operator algebra is commonly interpreted as a structure underlying a two-dimensional conformal field theory, allowing physics to form a bridge
Monstrous_moonshine
Straight path on a curved surface or a Riemannian manifold
the potential energy as reaction coordinate". The Journal of Chemical Physics. 128 (10): 104102. doi:10.1063/1.2834930. ISSN 0021-9606. PMID 18345872
Geodesic
General-purpose programming language
symbols for arithmetic operators (+, -, *, /), the floor-division operator //, and the modulo operator %. (With the modulo operator, a remainder can be negative
Python_(programming_language)
Performing order of mathematical operations
Common operator notation (for a more formal description) Hyperoperation Logical connective#Order of precedence Operator associativity Operator overloading
Order_of_operations
Subset of artificial intelligence
rudimentary reinforcement learning. It was repetitively "trained" by a human operator/teacher to recognise patterns and equipped with a "goof" button to cause
Machine_learning
Conserved physical quantity; rotational analogue of linear momentum
discussion below of the angular momentum operators as the generators of rotations.) However, in quantum physics, there is another type of angular momentum
Angular_momentum
OPERATOR PHYSICS
OPERATOR PHYSICS
Boy/Male
Hindu
Great orator
Boy/Male
Biblical
An orator.
Girl/Female
Biblical
An orator, an interpreter.
Boy/Male
Tamil
Orator
Boy/Male
Hindu, Indian, Kannada, Marathi, Tamil, Telugu
Orator
Boy/Male
Arabic
Orator; Speaker
Boy/Male
Muslim/Islamic
Orator Preacher
Biblical
an orator
Boy/Male
Tamil
Vakpati | வாகà¯à®ªà®¤à®¿
Great orator
Vakpati | வாகà¯à®ªà®¤à®¿
Boy/Male
Arabic
Orator; Speaker
Boy/Male
Arabic, Indian, Muslim
Orator; Preacher
Girl/Female
Assamese, Hindu, Indian, Tamil
Magnificent Poetess; Orator
Boy/Male
Muslim
Orator, Preacher, Religious minister
Girl/Female
Biblical
An orator, a word.
Girl/Female
Hindu, Indian, Sindhi, Tamil
Magnificent Poetess; Orator
Boy/Male
Hindu, Indian, Malayalam, Marathi
Great Orator
Girl/Female
Arabic
Orator; Preacher
Boy/Male
Muslim
Orator, Preacher, Religious minister
Girl/Female
Arabic
Orator; Preacher
Boy/Male
Arabic, Muslim
Orator; Preacher
OPERATOR PHYSICS
OPERATOR PHYSICS
Girl/Female
Indian, Punjabi, Sikh
Dominion of a Singer or a Lotus
Male
Arthurian
, a rogue knight.
Boy/Male
Indian, Punjabi, Sikh
Obedient
Boy/Male
Biblical
Clearness, oil.
Girl/Female
Christian, German, Greek, Indian, Italian, Latin, Spanish
The Lord's; Belongs to the Lord; Belonging to the Lord
Surname or Lastname
English
English : unexplained. Possibly a metonymic occupational name for a waterman on the Thames. The name is found in the 16th and 17th centuries in and around London.James Skiffe came from London, England, to Lynn, MA, in about 1635. Subsequently the family settled in Sandwich, MA.
Boy/Male
American, Australian, British, English, German, Norse, Norwegian, Scandinavian
Powerful Army; Strong Counselor; From the Ancient Personal Name Ragnar
Surname or Lastname
English
English : topographic name for someone who lived in a muddy place, from Middle English slott ‘mud’, ‘slime’.Swedish and Danish : ornamental name from slot(t) ‘palace’.Variant spelling of Dutch Slot, a metonymic occupational name for a locksmith, from Middle Dutch slo(e)t ‘lock’, ‘clasp’.Americanized form of Czech and Slovak slota ‘bad weather’, ‘evil person’, ‘witch’.
Girl/Female
Indian
Built; Construction; Creative Art; All Creation
Boy/Male
Indian, Sanskrit
King of the Ganges River
OPERATOR PHYSICS
OPERATOR PHYSICS
OPERATOR PHYSICS
OPERATOR PHYSICS
OPERATOR PHYSICS
n.
A dealer in stocks or any commodity for speculative purposes; a speculator.
v. t.
To put into, or to continue in, operation or activity; to work; as, to operate a machine.
n.
The method of working; mode of action.
n.
Something to be done; some transformation to be made upon quantities, the transformation being indicated either by rules or symbols.
n.
In the University of Oxford, an examiner for moderations; at Cambridge, the superintendant of examinations for degrees; at Dublin, either the first (senior) or second (junior) in rank in an examination for the degree of Bachelor of Arts.
n.
The act or process of operating; agency; the exertion of power, physical, mechanical, or moral.
n.
One fond of his own opinious; one who holds an opinion.
n.
Operation.
n.
A mechamical arrangement for regulating motion in a machine, or producing equality of effect.
n.
Effect produced; influence.
n.
One who, or that which, operates or produces an effect.
n.
That which is operated or accomplished; an effect brought about in accordance with a definite plan; as, military or naval operations.
n.
Any methodical action of the hand, or of the hand with instruments, on the human body, to produce a curative or remedial effect, as in amputation, etc.
imp. & p. p.
of Operate
n.
The officer who presides over an assembly to preserve order, propose questions, regulate the proceedings, and declare the votes.
n.
A laboratory.
n.
An officer who is the voice of the university upon all public occasions, who writes, reads, and records all letters of a public nature, presents, with an appropriate address, those persons on whom honorary degrees are to be conferred, and performs other like duties; -- called also public orator.
a.
Alt. of Operatical
n.
The symbol that expresses the operation to be performed; -- called also facient.
n.
One who performs some act upon the human body by means of the hand, or with instruments.