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Operator in quantum mechanics
where the total number of particles may not be preserved, the number operator is the observable that counts the number of particles. The following is
Particle_number_operator
Number of particles in a thermodynamic system
thermodynamics, the particle number (symbol N) of a thermodynamic system is the number of constituent particles in that system. The particle number is a fundamental
Particle_number
Transient quantum fluctuation (physics)
a particle is considered to be an eigenstate of the particle number operator a†a, where a is the particle annihilation operator and a† the particle creation
Virtual_particle
Number-state in quantum mechanics
{\displaystyle n_{{\mathbf {k} }_{i}}} denotes the number of particles in the i-th state ki, and the particle number operator for the i-th state, N k i ^ {\displaystyle
Fock_state
Operators useful in quantum mechanics
oscillators and many-particle systems. An annihilation operator (usually denoted a ^ {\displaystyle {\hat {a}}} ) lowers the number of particles in a given state
Creation and annihilation operators
Creation_and_annihilation_operators
Raising and lowering operators in quantum mechanics
of a ladder operator: the incrementing or decrementing of the eigenvalue of another operator (in this case the particle number operator). Confusion arises
Ladder_operator
Statistical ensemble of particles in thermodynamic equilibrium
energy operator (Hamiltonian), N̂1 is the system's total particle number operator for particles of type 1, N̂2 is the total particle number operator for
Grand_canonical_ensemble
Formulation of the quantum many-body problem
single-particle state with a certain number of identical particles. The second quantization formalism introduces the creation and annihilation operators to
Second_quantization
Intrinsic quantum property of particles
direction may change. These are indicated by assigning the particle a spin quantum number. The SI units of spin are the same as classical angular momentum
Spin_(physics)
Quantum operator for the sum of energies of a system
is the kinetic energy operator of particle n {\displaystyle n} , ∇ n {\displaystyle \nabla _{n}} is the gradient for particle n {\displaystyle n} , and
Hamiltonian (quantum mechanics)
Hamiltonian_(quantum_mechanics)
Mathematical approach to quantum optics
phase space, because typical optical observables, such as the particle number operator, are naturally expressed in normal order. It is named after George
Glauber–Sudarshan P representation
Glauber–Sudarshan_P_representation
Quantum mechanical operator related to rotational symmetry
quantum-mechanical operators. In the special case of a single particle with no electric charge and no spin, the orbital angular momentum operator can be written
Angular_momentum_operator
Research apparatus for particle physics
A particle accelerator is a machine that uses electromagnetic fields to propel ions to very high speeds and energies to contain them in well-defined beams
Particle_accelerator
Idealization of a large number of atomic-sized systems
energy operator H ^ {\displaystyle {\hat {H}}} (Hamiltonian). The grand canonical ensemble is additionally a function of the particle number, measured
Ensemble (mathematical physics)
Ensemble_(mathematical_physics)
Type of state in thermal systems
N\right)}}{Z(\beta ,\mu )}}} where H is the Hamiltonian operator and N is the particle number operator (or charge operator, if we wish to be more general) and Z ( β
KMS_state
Quasiparticle of mechanical vibrations
define particle number operator as N = ∑ α a α † a α . {\displaystyle N=\sum _{\alpha }{a_{\alpha }}^{\dagger }a_{\alpha }.} The number operator commutes
Phonon
Mathematics of a particle physics model
seen to add one particle, because it will add 1 to the eigenvalue of the a-particle number operator, and the momentum of that particle ought to be p since
Mathematical formulation of the Standard Model
Mathematical_formulation_of_the_Standard_Model
Operator in quantum mechanics
mechanics, the position operator is the operator that corresponds to the position observable of a particle. When the position operator is considered with a
Position_operator
Operator shifting particles and fields by a certain amount in a certain direction
In quantum mechanics, a translation operator is defined as an operator which shifts particles and fields by a certain amount in a certain direction. It
Translation operator (quantum mechanics)
Translation_operator_(quantum_mechanics)
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
Statistical mechanics of quantum-mechanical systems
_{i}N_{i}-H)}\right)}}.} Here, the N1, N2, ... are the particle number operators for the different species of particles that are exchanged with the reservoir. Unlike
Quantum_statistical_mechanics
Notation for conserved quantities in physics and chemistry
a spin quantum number without relying on classical models set the stage for the development of quantum numbers for elementary particles in the remainder
Quantum_number
Method of hydrodynamics simulation
cost of SPH simulations per number of particles is significantly less than the cost of grid-based simulations per number of cells when the metric of interest
Smoothed-particle hydrodynamics
Smoothed-particle_hydrodynamics
Theoretical model of the vacuum
annihilation with creation adds a constant to the negative energy particle number. The number operator for a Fermi field is: N = a † a = 1 − a a † {\displaystyle
Dirac_sea
Spontaneous breakdown of an unstable subatomic particle into other particles
In particle physics, particle decay is the spontaneous process of one unstable subatomic particle transforming into multiple other particles. The particles
Particle_decay
Species of elementary particle
In particle physics, flavour or flavor refers to the species of an elementary particle. The Standard Model counts six flavours of quarks and six flavours
Flavour_(particle_physics)
Type of particle charge found in the Standard Model
In particle physics, the hypercharge (a portmanteau of hyperonic and charge) Y of a particle is a quantum number conserved under the strong interaction
Hypercharge
Energy quantum particles contribute to themselves
over which a dressed particle behaves as if it were a single particle with well-defined momentum and energy. The self-energy operator (often denoted by Σ
Self-energy
Particle with opposite charges
In particle physics, every type of particle of "ordinary" matter (as opposed to antimatter) is associated with an antiparticle with the same mass but with
Antiparticle
Iterative simulation method
In computational science, particle swarm optimization (PSO) is a computational method that optimizes a problem by iteratively trying to improve a population
Particle_swarm_optimization
Theorem in quantum mechanics
intrinsic spin of a particle (angular momentum not due to the orbital motion) and the quantum particle statistics of collections of such particles is a consequence
Spin–statistics_theorem
Elementary particle involved with rest mass
Higgs boson, sometimes called the Higgs particle, is an elementary particle in the Standard Model of particle physics produced by the quantum excitation
Higgs_boson
Operator in quantum mechanics
{mc^{2}}{\hbar }}\right)^{2}\Psi } The energy operator is easily derived from using the free particle wave function (plane wave solution to Schrödinger's
Energy_operator
Elementary particles with a spin of 1/2
of all elementary particles. All known fermions, the particles that constitute ordinary matter, have a spin of 1/2. The spin number describes how many
Spin_1/2
Concept in quantum mechanics of perfectly substitutable particles
quantum mechanics, indistinguishable particles (also called identical or indiscernible particles) are particles that cannot be distinguished from one
Indistinguishable_particles
Mathematical description of quantum state
simple matter to note that, for example, the momentum operator of the i'th particle in a n-particle system is not a generator of any symmetry in nature
Wave_function
Description of a quantum-mechanical system
Klein–Gordon operator and in turn introducing Dirac matrices. In a modern context, the Klein–Gordon equation describes spin-less particles, while the Dirac
Schrödinger_equation
Property of particles related to spin
chirality operator with the helicity operator. Since the helicity of massive particles is frame-dependent, it might seem that the same particle would interact
Chirality_(physics)
Process in quantum mechanical theories
\omega _{k}N_{k},} where Nk may be interpreted as the number operator giving the number of particles in a state with momentum k. This Hamiltonian differs
Canonical_quantization
Mathematical entity to describe the probability of each possible measurement on a system
as the energy or momentum of a particle) is associated with a mathematical operator called the observable. The operator serves as a linear function that
Quantum_state
Raising and lowering operators
time. We specify the operators S 2 {\displaystyle S^{2}} and S z {\displaystyle S_{z}} . The creation of a particle and anti-particle from a boson is defined
Anti-symmetric_operator
Multi particle state space
the quantum states space of a variable or unknown number of identical particles from a single particle Hilbert space H. It is named after V. A. Fock who
Fock_space
Symmetry of spatially mirrored systems
(−1)F symmetry, where F is the fermion number operator counting how many fermions are in a state. Since all particles in the Standard Model satisfy F = B
Parity_(physics)
High-temperature expansion in statistical mechanics
{\displaystyle N} -particle operator. However, the many-body as well as quantum-optical interactions couple the N {\displaystyle N} -particle quantities to
Cluster_expansion
Quantum mechanical operator interchanging particle states as arguments to a function
acts on states in Fock space. The exchange operator acts by switching the labels on any two identical particles described by the joint position quantum state
Exchange_operator
Term in quantum field theory
involutive operator where F is the fermion number operator. For the example of particles in the Standard Model, it is equal to the sum of the lepton number plus
(−1)F
Instrument used for measuring ionizing radiation
α- and β-particles. A skilled operator can use varying distance from a radiation source to differentiate between α- and high energy β-particles. The "pancake"
Geiger_counter
Function acting on the space of physical states in physics
observable, for particle in region R. The expectation value ⟨ A ^ ⟩ {\displaystyle \left\langle {\hat {A}}\right\rangle } of the operator A ^ {\displaystyle
Operator_(physics)
Quantum number relating the quantity of quarks and antiquarks in a system
In particle physics, the baryon number (B) is an additive quantum number of a system. It is defined as B = 1 3 ( n q − n q ¯ ) , {\displaystyle B={\frac
Baryon_number
hydrogen identical particles angular momentum angular momentum operator rotational invariance rotational symmetry rotation operator translational symmetry
List of mathematical topics in quantum theory
List_of_mathematical_topics_in_quantum_theory
eigenstates. Momentum of each particle has stabilized and is again a good quantum number a long time after the collision. An operator, O {\displaystyle O} ,
Good_quantum_number
Quantum mechanical model
and particle-like properties. The particle-like properties of the phonon are best understood using the methods of second quantization and operator techniques
Quantum_harmonic_oscillator
Quantum number related to the weak interaction
nuclear physics and particle physics, isospin ( I ) is a quantum number related to the up- and down quark content of the particle. Isospin is also known
Isospin
Function in quantum field theory showing probability amplitudes of moving particles
Propagators may also be viewed as the inverse of the wave operator appropriate to the particle, and are, therefore, often called (causal) Green's functions
Propagator
Concept in statistics
to symmetric operator ordering. In quantum optics specifically, often the operators of interest, especially the particle number operator, is naturally
Quasiprobability_distribution
Equation of statistical mechanics
as energy, charge or particle number. The equation arises not by analyzing the individual positions and momenta of each particle in the fluid but rather
Boltzmann_equation
Quantum mechanics taking into account particles near or at the speed of light
operator Ĥ corresponding to the system. The solution is a complex-valued wavefunction ψ(r, t), a function of the 3D position vector r of the particle
Relativistic quantum mechanics
Relativistic_quantum_mechanics
Description of physical properties at the atomic and subatomic scale
complex number, known as a probability amplitude. This is known as the Born rule, named after physicist Max Born. For example, a quantum particle like an
Quantum_mechanics
Fermion that is its own antiparticle
In particle physics a Majorana fermion (/maɪəˈrɑːnə/) or Majorana particle is a fermion that is its own antiparticle. They were hypothesised by Ettore
Majorana_fermion
Component of an atomic nucleus
nucleus. The number of nucleons in a nucleus defines the atom's mass number. Until the 1960s, nucleons were thought to be elementary particles, not made
Nucleon
Physical fields obeying the Schrödinger equation
Schrödinger equation for identical particles, the field theory is more suitable for situations where the particle number changes. A Schrödinger field is
Schrödinger_field
Collision of a particle and its antiparticle
In particle physics, annihilation is the process that occurs when a subatomic particle collides with its respective antiparticle to produce other particles
Annihilation
Elementary particle with extremely low mass
(/njuːˈtriːnoʊ/ new-TREE-noh; denoted by the Greek letter ν) is an elementary particle that interacts via the weak interaction and gravity. The neutrino is so
Neutrino
Quantum mechanical transmutation of neutral particles
In particle physics, neutral particle oscillation is the transmutation of a particle with zero electric charge into another neutral particle due to a
Neutral_particle_oscillation
Eigenvalue problem for the Laplace operator
Laplace operator, –k2 is the eigenvalue, and f is the (eigen)function. When the equation is applied to waves, k is known as the wave number. The Helmholtz
Helmholtz_equation
Random motion of particles suspended in a fluid
Brownian motion is the random motion of particles suspended in a medium (a liquid or a gas). The traditional mathematical formulation of Brownian motion
Brownian_motion
Properties underlying modern physics
probability of finding the particle somewhere with some spin) must be invariant under these transformations. The inverse of a unitary operator is its Hermitian
Symmetry_in_quantum_mechanics
Particle that is not bound by an external force
In physics, a free particle is a particle that, in some sense, is not bound by an external force, or equivalently not in a region where its potential energy
Free_particle
Hypothetical faster-than-light particle
or tachyonic particle is a hypothetical particle that always travels faster than light. Physicists posit that faster-than-light particles cannot exist
Tachyon
box Particle in a one-dimensional lattice Particle in a ring Particle in a spherically symmetric potential Particle number Particle number operator Particle
Index_of_physics_articles_(P)
Unitary operation that transforms a particle in its antiparticle
{C}}^{\dagger }=\mathbf {1} .} By acting on the particle twice with the C {\displaystyle {\mathcal {C}}} operator, C 2 | ψ ⟩ = C | ψ ¯ ⟩ = | ψ ⟩ , {\displaystyle
C_parity
Matrix representing the effect of scattering on a physical system
diagrams. In scattering theory, the S-matrix is an operator mapping free particle in-states to free particle out-states (scattering channels) in the Heisenberg
S-matrix
Pictorial representation of the behavior of subatomic particles
probability amplitudes in theoretical particle physics requires the use of large, complicated integrals over a large number of variables. Feynman diagrams instead
Feynman_diagram
Theory of subatomic structure
stimulated a number of major developments in pure mathematics. Because string theory potentially provides a unified description of gravity and particle physics
String_theory
Elementary particle or quantum of light
(from Ancient Greek φῶς, φωτός (phôs, phōtós) 'light') is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic
Photon
Quantum number related to the weak interaction
In particle physics, weak isospin is a quantum number relating to the electrically charged part of the weak interaction. Particles with nonzero weak isospin
Weak_isospin
Used to count, measure, and label
texts this word often refers to the number zero. In a similar vein, Pāṇini (5th century BC) used the null (zero) operator in the Ashtadhyayi, an early example
Number
Specific quantum state of a quantum harmonic oscillator
solutions by a particle oscillating with an amplitude equivalent to the displacement. These states, expressed as eigenvectors of the lowering operator and forming
Coherent_state
Special low-energy state in quantum mechanics
originally meant a linked set of particles whose net angular momentum is zero, that is, whose overall spin quantum number s = 0 {\displaystyle s=0} . As
Singlet_state
Mathematically, it is represented by a Hermitian operator. Exchange Intrinsically identical particles If the intrinsic properties (properties that can
Glossary of elementary quantum mechanics
Glossary_of_elementary_quantum_mechanics
Quantum number denoting orbital angular momentum
Introduction to quantum mechanics Particle in a spherically symmetric potential Angular momentum coupling Angular momentum operator Clebsch–Gordan coefficients
Azimuthal_quantum_number
Quantum operator
is why, it is first shown how the translation operator is acting on a particle at position x (the particle is then in the state | x ⟩ {\displaystyle |x\rangle
Rotation operator (quantum mechanics)
Rotation_operator_(quantum_mechanics)
Type of Monte Carlo algorithms for signal processing and statistical inference
Particle filters, also known as sequential Monte Carlo methods, are a set of Monte Carlo algorithms used to find approximate solutions for filtering problems
Particle_filter
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
Algebra based on a vector space with a quadratic form
Cl(V, Q) is nondegenerate if and only if it is nondegenerate on V. The operator of left (respectively right) Clifford multiplication by the transpose at
Clifford_algebra
Physics phenomenon
quantum state of each particle in a group cannot be described independently of the state of the others, even when the particles are separated by a large
Quantum_entanglement
Function in thermodynamics and statistical physics
exchange heat with the environment at fixed temperature, volume, and number of particles. The grand canonical partition function applies to a grand canonical
Partition function (statistical mechanics)
Partition_function_(statistical_mechanics)
Hypothetical particle decay process of a proton
stable because baryon number is conserved. Since protons are the lightest baryons in the model, they cannot decay into other particles on their own and are
Proton_decay
Mathematical structures that allow quantum mechanics to be explained
general case of a system of identical particles. In a system of identical particles, let P be known as exchange operator that acts on the wavefunction as:
Mathematical formulation of quantum mechanics
Mathematical_formulation_of_quantum_mechanics
Value for the flow of probability in quantum mechanics
vector of the particle with corresponding spin magnetic moment μS and spin quantum number s. It is doubtful if this formula is valid for particles with an interior
Probability_current
Relativistic quantum mechanical wave equation
In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including
Dirac_equation
Quantum state with all observables independent of time
time elapses, in every observable way. For a single-particle Hamiltonian, this means that the particle has a constant probability distribution for its position
Stationary_state
Quantum mechanical equation of motion of charged particles in magnetic field
{B} \,,} where L ^ {\textstyle \mathbf {\hat {L}} } is the particle angular momentum operator and we neglected terms in the magnetic field squared B 2 {\textstyle
Pauli_equation
Physics property associated with symmetries
the formalism of particle theories, charge-like quantum numbers can sometimes be inverted by means of a charge conjugation operator called C. Charge conjugation
Charge_(physics)
Conserved physical quantity; rotational analogue of linear momentum
called spin angular momentum, represented by the spin operator S. Spin is often depicted as a particle literally spinning around an axis, but this is a misleading
Angular_momentum
Concept in physics
between them. This in turn restricts the types and hence number and density of virtual particle pairs which can form in the intervening vacuum and can result
Negative_energy
Mathematical approach to quantum physics
solutions, such as the hydrogen atom, the quantum harmonic oscillator and the particle in a box, are too idealized to adequately describe most systems. Using
Perturbation theory (quantum mechanics)
Perturbation_theory_(quantum_mechanics)
Application of mathematical methods to other fields
have become increasingly important in applications. Even fields such as number theory that are part of pure mathematics are now important in applications
Applied_mathematics
Property of a mass in motion
momentum are conjugate variables. For a single particle described in the position basis the momentum operator can be written as p = ℏ i ∇ = − i ℏ ∇ , {\displaystyle
Momentum
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
PARTICLE NUMBER-OPERATOR
PARTICLE NUMBER-OPERATOR
Male
French
Medieval French form of Latin Patricius, PATRICE means "patrician; of noble descent."
Girl/Female
Arabic, Hindu, Indian, Kannada, Muslim
Particle of Gold
Girl/Female
Indian
Minute particle, Beautiful
Surname or Lastname
English
English : perhaps a variant of Pamber, a habitational name from a place in Hampshire named Pamber, from Old English penn ‘fold’, ‘enclosure’ + beorg ‘hill’.
Surname or Lastname
English
English : occupational name for a summoner, an official who was responsible for ensuring the appearance of witnesses in court, Middle English sumner, sumnor.William Sumner came to Dorchester, MA, from England in about 1635. His descendants include U.S. Senator Charles Sumner, a major force in the struggle to end slavery, who was born in 1811 in Boston.
Girl/Female
Indian
Minute particle, Beautiful
Girl/Female
American, Arabic, Australian, British, Chinese, English, Hebrew
The Warmest Season of the Year; Summer Season; Name of the Season; Summer; The Hot Season of the Year
Male
English
English form of Norman Germanic Huncberct, possibly HUMBERT means "bright support."Â
Boy/Male
Hindu, Indian
Minute Particle
Girl/Female
Tamil
Anshika | அநà¯à®·à®¿à®•à®¾
Minute particle, Beautiful
Anshika | அநà¯à®·à®¿à®•à®¾
Girl/Female
Muslim American Arabic English Gaelic
Jewel. Amber stone.
Girl/Female
Muslim
Particle of gold
Female
Native American
Native American Algonquin name NUMEES means "sister."
Girl/Female
Arabic, Australian, Hebrew
Particle
Female
English
English name derived from the vocabulary word, summer, from Old English sumor, SUMMER means "summer," the hot season of the year.
Boy/Male
Hindu, Indian
Number
Surname or Lastname
English
English : habitational name from any of the various places so called from their situation on a stream with this name. Humber is a common prehistoric river name, of uncertain origin and meaning.
Girl/Female
Tamil
Ansika | அநà¯à®¸à¯€à®•à®¾
Minute particle, Beautiful
Ansika | அநà¯à®¸à¯€à®•à®¾
Girl/Female
English American
Born during the summer.
Male
German
German byname BAMBER means "short and fat."Â
PARTICLE NUMBER-OPERATOR
PARTICLE NUMBER-OPERATOR
Boy/Male
Australian, Basque, French, German, Polish, Romanian
Of the Sea; From the God Mars
Surname or Lastname
Scottish
Scottish : from a pet form of Rabb.English : from the Norman personal name Radbode, Rabbode, composed of the Germanic elements rÄd ‘counsel’, ‘advice’ + bodo, boto ‘messenger’, ‘lord’.Irish : mistranslation of Gaelic Ó CoinÃn, which is actually a variant of Ó Conáin or Ó Cuineáin (see Cunneen), as if it were from coinÃn ‘rabbit’, although in fact it is from a diminutive of cano ‘hound’, ‘wolf’.
Boy/Male
Indian
Of the Aryan race, Ancient
Girl/Female
Hindu, Indian, Malayalam, Marathi
Soft Natured
Girl/Female
Hindu
Most respectable
Girl/Female
British, English, Hebrew, Irish
Rhyming Variant of Molly; Bitterness; Star of the Sea; Small
Boy/Male
Australian, Polish
A Rower; An Oarsman
Girl/Female
Hindu, Indian, Kashmiri
Different Kinds
Girl/Female
Tamil
Woman, Young girl
Female
Egyptian
, an lady of rank in the XIIth dynasty.
PARTICLE NUMBER-OPERATOR
PARTICLE NUMBER-OPERATOR
PARTICLE NUMBER-OPERATOR
PARTICLE NUMBER-OPERATOR
PARTICLE NUMBER-OPERATOR
a.
See Partible.
v. t.
To furnish with timber; -- chiefly used in the past participle.
n.
To accuse or charge by an exhibition of articles.
a.
Bound by articles; apprenticed; as, an articled clerk.
imp. & p. p.
of Number
n.
One of the three words, a, an, the, used before nouns to limit or define their application. A (or an) is called the indefinite article, the the definite article.
n.
A minute part or portion of matter; a morsel; a little bit; an atom; a jot; as, a particle of sand, of wood, of dust.
n.
A numeral; a word or character denoting a number; as, to put a number on a door.
a.
Of or pertaining to umber; like umber; as, umbery gold.
n.
A particular one of various things; as, an article of merchandise; salt is a necessary article.
b. t.
To fill or encumber with lumber; as, to lumber up a room.
n.
Pertaining to a subordinate portion; as, a compound umbel is made up of a several partial umbels; a leaflet is often supported by a partial petiole.
n.
To amount; to equal in number; to contain; to consist of; as, the army numbers fifty thousand.
imp. & p. p.
of Article
n.
Number; -- often abbrev. No.
v. i.
To agree by articles; to stipulate; to bargain; to covenant.
n.
To formulate in articles; to set forth in distinct particulars.
n.
To bind by articles of covenant or stipulation; as, to article an apprentice to a mechanic.
n.
To give or apply a number or numbers to; to assign the place of in a series by order of number; to designate the place of by a number or numeral; as, to number the houses in a street, or the apartments in a building.
n.
Any very small portion or part; the smallest portion; as, he has not a particle of patriotism or virtue.