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Number-state in quantum mechanics
In quantum mechanics, a Fock state or number state is a quantum state that is an element of a Fock space with a well-defined number of particles (or quanta)
Fock_state
Multi particle state space
respectively). A general state in Fock space is a linear combination of n-particle states, one for each n. Technically, the Fock space is (the Hilbert space
Fock_space
Formulation of the quantum many-body problem
by Pascual Jordan and Vladimir Fock. In this approach, the quantum many-body states are represented in the Fock state basis, which are constructed by
Second_quantization
Russian physicist (1898–1974)
Klein–Gordon equation. He gave his name to Fock space, the Fock representation and Fock state, and developed the Hartree–Fock method in 1930. He made many subsequent
Vladimir_Fock
Concept in statistics
however, the quantum system has no classical analog, e.g. an incoherent Fock state or entangled system, then P is negative somewhere or more singular than
Quasiprobability_distribution
Training ship in the German Navy
Gorch Fock is a tall ship of the German Navy, launched in 1958 as a replacement for the original Gorch Fock (1933) launched in 1933 which was taken as
German training ship Gorch Fock (1958)
German_training_ship_Gorch_Fock_(1958)
Approximation method in quantum physics
the Hartree–Fock (HF) method is used for approximating the wave function and the energy of a quantum many-body system in a stationary state. It is named
Hartree–Fock_method
Candidate unified theory of physics
Moreover, it comprises quantum objects like wave functions and a fermionic Fock state. Inspired by the Lagrangian formulation of classical field theory, the
Causal_fermion_systems
Specific quantum state of a quantum harmonic oscillator
Fock state (e.g. a single photon) is the most particle-like state; it has a fixed number of particles, and phase is indeterminate. A coherent state distributes
Coherent_state
Vladimir Fock: Fock matrix Fock operator Fock model Fock representation Fock space Bargmann–Fock space Fock state Fock symmetry Fock–Lorentz symmetry Fock–Schwinger
List of things named after Vladimir Fock
List_of_things_named_after_Vladimir_Fock
Mathematical approach to quantum optics
however, the quantum system has no classical analog, e.g. an incoherent Fock state or entangled system, then P is negative somewhere or more singular than
Glauber–Sudarshan P representation
Glauber–Sudarshan_P_representation
German museum ship
Gorch Fock I (ex Tovarishch, ex Gorch Fock) is a German three-mast barque, the first of a series built as school ships for the German Reichsmarine in 1933
Gorch_Fock_(1933)
Formulation to quantize gauge field theories in physics
into one object (a Fock state), and then describe the "evolution" of this state over time using the interaction picture. The Fock space is spanned by
BRST_quantization
Operator in quantum mechanics
\rangle _{\nu }=|\phi _{1},\phi _{2},\cdots ,\phi _{n}\rangle _{\nu }} be a Fock state, composed of single-particle states | ϕ i ⟩ {\displaystyle |\phi _{i}\rangle
Particle_number_operator
Type of quantum state
explicitly shows that the pure SMSV consists entirely of even-photon Fock state superpositions. Single mode squeezed states are typically generated by
Squeezed_coherent_state
Basic unit of quantum information
of the classic binary bit. A qubit can be physically realized with a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems
Qubit
Physics phenomenon
mode". Finally, there also exist twin Fock states for bosonic modes, which can be created by feeding a Fock state into two arms leading to a beam splitter
Quantum_entanglement
Quantum state, of opposed conditions
defined in the number (Fock) basis. Notice that if we add the two states together, the resulting cat state only contains even Fock state terms: | c a t e ⟩
Cat_state
Concept in quantum optics
Bellini, Marco (2004). "Tomographic reconstruction of the single-photon Fock state by high-frequency homodyne detection". Physical Review A. 70 (5) 053821
Spontaneous parametric down-conversion
Spontaneous_parametric_down-conversion
Elementary particle or quantum of light
Collider. In modern physics notation, the quantum state of the electromagnetic field is written as a Fock state, a tensor product of the states for each electromagnetic
Photon
Mathematical entity to describe the probability of each possible measurement on a system
quantum systems in a Fock space. As a tool for physics, quantum states grew out of states in classical mechanics. A classical dynamical state consists of a set
Quantum_state
Optical device which splits a beam of light in two
e. the states |01⟩ and |10⟩ in the occupation number representation (Fock state) of two modes. Using these resources it is possible to implement any single
Beam_splitter
Branch of chemistry
single Fock state that minimizes the energy. NP-hard or NP-complete as demonstrated by embedding instances of the Ising model into Hartree-Fock calculations
Computational_chemistry
Algorithm to be run on quantum computers
predicted the sampling problem had similar complexity for inputs other than Fock-state photons and identified a transition in computational complexity from classically
Quantum_algorithm
Dutch politician and diplomat (1858–1941)
Dirk Fock (19 June 1858 – 17 October 1941) was a Dutch politician and diplomat of the defunct Liberal State Party (LSP) now merged into the People's Party
Dirk_Fock
Number of particles in a thermodynamic system
the particle number operator (see Fock state) is conjugate to the phase of the classical wave (see coherent state). One measure of air pollution used
Particle_number
List of terms created from a person's name
architect – Floriana, Floriana Lines Vladimir Fock, Russian physicist – Fock space, Fock state, Hartree-Fock method Jack Foley, American sound-effects artist
List_of_eponyms_(A–K)
Model of quantum optics
by Fock states with n {\displaystyle n} photons, denoted by | n ⟩ {\displaystyle |n\rangle } . These states can be constructed from the vacuum state |
Dicke_model
Wigner distribution function in physics as opposed to in signal processing
inference. A very big cat state, with 10 cats separated at α = 10 {\displaystyle \alpha =10} . Fock states Superpositioned Fock states, for ( n , m ) =
Wigner quasiprobability distribution
Wigner_quasiprobability_distribution
Lvovsky
single-photon Fock state. Observation of quantum memory for squeezed light. A method for optical quantum process tomography by coherent state probing. Producing
Alexander_Lvovsky
Joint Institute for Nuclear Research Vladimir Fock, developed the Fock space, Fock state and the Hartree–Fock method in quantum mechanics Ilya Frank, explained
List_of_Russian_scientists
Interference effect of two photons
described by the Fock states, so, for example | 0 ⟩ a {\displaystyle |0\rangle _{a}} corresponds to mode a empty (the vacuum state), and inserting one
Hong–Ou–Mandel_effect
Quantization giving rise to photons
})^{n}|0\rangle =n(a^{\dagger })^{n}|0\rangle .} A photon number state (or a Fock state) is an eigenstate of the number operator. This is why the formalism
Quantization of the electromagnetic field
Quantization_of_the_electromagnetic_field
Set of methods in computational chemistry
computational chemistry, post–Hartree–Fock (post-HF) methods are the set of methods developed to improve on the Hartree–Fock (HF), or self-consistent field (SCF)
Post–Hartree–Fock
Theorem in quantum chemistry
structure. It states that within the common Hartree–Fock approximation, the electronic ground state does not directly mix or interact with electronic states
Brillouin's_theorem
Phenomenon in quantum optics
down-conversion. Degree of coherence Fock state Hong–Ou–Mandel effect Hanbury Brown and Twiss effect Squeezed coherent state Article based on text from Qwiki
Photon_antibunching
Statistical study of photon counting
}\right\vert }^{2}}{2}}|n\rangle } By projecting the coherent state onto the Fock state | n ⟩ {\displaystyle |n\rangle } , we can find the probability
Photon_statistics
Concept in computational chemistry
Configuration interaction (CI) is a post-Hartree–Fock linear variational method for solving the nonrelativistic Schrödinger equation within the Born–Oppenheimer
Configuration_interaction
Theorem in quantum mechanics
Koopmans' theorem states that in closed-shell Hartree–Fock theory (HF), the first ionization energy of a molecular system is equal to the negative of the
Koopmans'_theorem
Method in ab initio Quantum Chemistry
quantum chemistry post-Hartree–Fock ab initio methods in the field of computational chemistry. It improves on the Hartree–Fock method by adding electron correlation
Møller–Plesset perturbation theory
Møller–Plesset_perturbation_theory
Joint Institute for Nuclear Research Vladimir Fock, developed the Fock space, Fock state and the Hartree–Fock method in quantum mechanics Ilya Frank, explained
List_of_Russian_physicists
Category of computational quantum chemistry technique
equivalent Hartree–Fock calculation. Local DFT methods that do not include Hartree–Fock exchange can scale better than Hartree–Fock.[citation needed] The
Ab initio quantum chemistry methods
Ab_initio_quantum_chemistry_methods
Method for calculating open-shell systems
Unrestricted Hartree–Fock (UHF) theory is the most common molecular orbital method for open shell molecules where the number of electrons of each spin
Unrestricted_Hartree–Fock
such as Hartree–Fock, Post–Hartree–Fock, density-functional theory, and relativistic formalisms for molecular, biological, and solid-state chemistry systems
List of computational chemistry software
List_of_computational_chemistry_software
Relativistic wave equation in quantum mechanics
sometimes referred to as Schrödinger's relativistic equation or the Klein–Gordon–Fock equation. The first to discover the equation in December 1925, but not publish
Klein–Gordon_equation
mechanics Observable Operator (physics) Quantum state Pure state Fock state, Fock space Density state Coherent state Heisenberg picture Density matrix Quantum
List of functional analysis topics
List_of_functional_analysis_topics
Quantum electromechanical process
spontaneous decay occurs when the excited state of the atom emits a photon back into the vacuum Fock state of the field | excited ⟩ ⊗ | { 0 } ⟩ ⇒ | ground
Resonance_fluorescence
Dutch-born American actress (1924–2008)
Nina Foch (/fɒʃ/ FOSH; born Nina Consuelo Maud Fock; April 20, 1924 – December 5, 2008) was an American actress who later became a drama instructor. Her
Nina_Foch
Joint Institute for Nuclear Research Vladimir Fock, developed the Fock space, Fock state and the Hartree–Fock method in quantum mechanics Ilya Frank, explained
List_of_Russian_people
the methods of quantum chemistry. Most include the Hartree–Fock (HF) and some post-Hartree–Fock methods. They may also include density functional theory
List of quantum chemistry and solid-state physics software
List_of_quantum_chemistry_and_solid-state_physics_software
collapse zero-point energy bound state coherent state squeezed coherent state density state Fock state, Fock space vacuum state quasinormal mode no-cloning
List of mathematical topics in quantum theory
List_of_mathematical_topics_in_quantum_theory
Macroscopic processes showing quantum behavior
achieved cooling to the quantum ground state ( n = 0 {\displaystyle n=0} ), preparation of a single-phonon Fock state ( n = 1 {\displaystyle n=1} ), and the
Macroscopic_quantum_phenomena
Model of interacting spinless bosons on a lattice
where m {\displaystyle m} is an integer that labels the filling of the Fock state. The perturbative piece can be treated with second-order perturbation
Bose–Hubbard_model
Public research university in Russia
mathematician Leonard Euler, mathematician Vera Faddeeva, mathematician Vladimir Fock, physicist Sergey Fomin, Russian-American mathematician Leonid Frankfurt
Saint Petersburg State University
Saint_Petersburg_State_University
open-shell Hartree–Fock, ROHF) or permit complete variational freedom (unrestricted Hartree–Fock UHF). In general, an N-electron Hartree–Fock wave function
Spin_contamination
Computational quantum mechanical modelling method to investigate electronic structure
low when compared to traditional methods, such as exchange only Hartree–Fock theory and its descendants that include electron correlation. Since, DFT
Density_functional_theory
Soviet American mathematician
arXiv:math/0302267, doi:10.1016/j.ansens.2004.11.001, S2CID 119144154 (with V. V. Fock) Fock, Vladimir; Goncharov, Alexander (2006). "Moduli spaces of local systems
Alexander_Goncharov
Structure of the atomic nucleus
nucleus by a rotation are just as good solutions for the Hartree–Fock problem. The ground state of the nucleus is then degenerate. A similar phenomenon happens
Nuclear_structure
Prime minister (1961–1965) Gyula Kállai, Prime minister (1965–1967) Jenő Fock, Prime minister (1967–1975) György Lázár, Prime minister (1975–1987) Károly
List of state leaders in the 20th century (1951–2000)
List_of_state_leaders_in_the_20th_century_(1951–2000)
The Minister of State (Dutch: Minister van Staat) is an honorary title in the Netherlands. The title is formally granted together with the style Excellency
Minister of State (Netherlands)
Minister_of_State_(Netherlands)
truncated configuration interaction, which is one of several post-Hartree–Fock ab initio quantum chemistry methods in the field of computational chemistry
Davidson_correction
Representation theory of the symplectic group
the symmetric Fock space S(H) is defined to be the Hilbert space completion of this direct sum. For ξ in H define the coherent state eξ by e ξ = ∑ k
Oscillator_representation
Technique in computational quantum field theory
particles. The state of the system then does not have a definite number of particles, but is instead a quantum-mechanical linear combination of Fock states,
Light_front_quantization
Method in quantum chemistry
qualitatively correct reference states of molecules in cases where Hartree–Fock and density functional theory are not adequate (e.g., for molecular ground
Multi-configurational self-consistent field
Multi-configurational_self-consistent_field
Set of functions used to represent the electronic wave function
functions) that is used to represent the electronic wave function in the Hartree–Fock method or density-functional theory in order to turn the partial differential
Basis_set_(chemistry)
Quantization procedure in quantum field theory
describing the bound-state structure of relativistic composite systems, needed for describing exclusive amplitudes, is the light-front Fock expansion which
Light-front quantization applications
Light-front_quantization_applications
Atom of helium
However, various approximations, such as the Hartree–Fock method, can be used to estimate the ground state energy and wavefunction of the atom. Historically
Helium_atom
Flyby anomaly Flying-spot scanner Flying wing Focal length Fock matrix Fock space Fock state Fock–Lorentz symmetry Focus (optics) Foe (unit) Fog bow Folded
Index_of_physics_articles_(F)
Chemistry based on quantum physics
John Lennard-Jones, and Vladimir Fock.[vague] The electronic structure of an atom or molecule is the quantum state of its electrons. The first step in
Quantum_chemistry
Romanian sail training ship
steel-hulled three-masted barque built on the plans of the Gorch Fock, the only sister ship of Gorch Fock built on the original 1933 plans. She has a length of 82
Mircea_(ship)
Procedure of coping with redundant degrees of freedom in physical field theories
{E} (u\mathbf {r} ,t)du.} The gauge condition of the Fock–Schwinger gauge (named after Vladimir Fock and Julian Schwinger; sometimes also called the relativistic
Gauge_fixing
Description of a quantum-mechanical system
space where the basis states are labeled by particle number, a so-called Fock space. The Schrödinger equation can then be formulated for quantum states
Schrödinger_equation
German Nazi politician and military leader (1893–1946)
introduced his sister-in-law, Baroness Carin von Kantzow (née Freiin von Fock). Estranged from her husband of 10 years, she had an eight-year-old son.
Hermann_Göring
American singer, songwriter, and actress (born 1993)
7, 2026. Hughes, William (April 15, 2026). "It's Ariana Grande's turn to Fock things up in the Focker-In-Law trailer". The A.V. Club. Retrieved May 23
Ariana_Grande
Danish mathematical physicist
atoms and molecules in the Thomas-Fermi model and the Hartree-Fock method), solid-state physics (the Bose-Einstein condensate, Bogoliubov transformation
Jan_Philip_Solovej
Clinical presentation
doi:10.1093/schbul/sbu099. ISSN 1745-1701. PMC 4332942. PMID 25103207. Föcking, Melanie; Dicker, Patrick; Lopez, Lorna M.; Cannon, Mary; Schäfer, Miriam
At_risk_mental_state
Danish politician (born 1965)
Josephine Fock (born 5 September 1965) is a former Danish politician who was a member of the Folketing for The Alternative from 2015 to 2018. She served
Josephine_Fock
German physicist
Mlynek, J.; Schiller, S. (11 July 2001). "Quantum State Reconstruction of the Single-Photon Fock State". Physical Review Letters. 87 (5) 050402. arXiv:quant-ph/0101051
Jürgen_Mlynek
Canadian theoretical physicist (1960–2025)
universal quantum computation when acting on a suitable multi-photon Fock state as initial state (KLM protocol). This was an important result for optics-based
Raymond_Laflamme
Tabular arrangement of the chemical elements
ISBN 978-3-540-07109-9. Retrieved 4 October 2013. Fricke, Burkhard (1977). "Dirac–Fock–Slater calculations for the elements Z = 100, fermium, to Z = 173" (PDF)
Periodic_table
Schwinger–Tomonaga equation Fock–Schwinger gauge Jordan–Schwinger map Rarita–Schwinger equation Lippmann–Schwinger equation Kubo–Martin–Schwinger state Schwinger boson
List of things named after Julian Schwinger
List_of_things_named_after_Julian_Schwinger
in the Brillouin zone. Calculations can use the Hartree–Fock method, some post-Hartree–Fock methods, particularly Møller–Plesset perturbation theory
Computational chemical methods in solid-state physics
Computational_chemical_methods_in_solid-state_physics
Mathematical tool in quantum physics
where the states summed over to make the density matrix are drawn from a Fock space. Quantum decoherence theory typically involves non-isolated quantum
Density_matrix
Approximating method in quantum mechanics
ground state wavefunction, and the expectation value of the energy in that state is an upper bound to the ground state energy. The Hartree–Fock method
Variational method (quantum mechanics)
Variational_method_(quantum_mechanics)
Concept in quantum mechanics
quantum mechanics. Its original form, due to Max Born and Vladimir Fock (1928), was stated as follows: A physical system remains in its instantaneous eigenstate
Adiabatic_theorem
Method for approximating many-body systems
many-body systems. Its most common use is as one of several post-Hartree–Fock ab initio quantum chemistry methods in the field of computational chemistry
Coupled_cluster
Quantum mechanical operator interchanging particle states as arguments to a function
states in Fock space. The exchange operator acts by switching the labels on any two identical particles described by the joint position quantum state | x 1
Exchange_operator
Swedish noble and alleged murderer
Metta (or Mätta) Charlotta Fock, née Ridderbjelke (10 June 1765 – 7 November 1810), was a Swedish noble and sentenced murderer. She was executed for murdering
Metta_Fock
Political party in the Netherlands
The Liberal State Party, "the Freedom League" (Dutch: Liberale Staatspartij "de Vrijheidsbond", LSP), was a conservative liberal political party in the
Liberal_State_Party
Equation in solid state physics
introduced them in 1927. Hartree method is one of the main ingredients of Hartree–Fock method, which improves on Hartree equations by including the exchange interaction
Hartree_equations
Russian mathematician (1912–1999)
Leningrad State University. His advisors there were Vladimir Fock, a physicist, and Boris Delaunay, a mathematician. In 1933 Aleksandrov worked at the State Optical
Aleksandr Aleksandrov (mathematician)
Aleksandr_Aleksandrov_(mathematician)
Technique in computational quantum field theory
expansions in products of single-particle basis functions to represent the Fock-state wave functions. Typically, the longitudinal ( x − {\displaystyle x^{-}}
Light-front computational methods
Light-front_computational_methods
Topics referred to by the same term
Post-Hartree–Fock, the set of methods developed to improve on the Hartree–Fock method Restricted open-shell Hartree–Fock, a variant of Hartree–Fock method for
Hartree_(disambiguation)
of the Saint Petersburg State University in 1905. He left the post in 1910. Under the leadership of Borgman, the V. A. Fock Institute of Physics was
Ivan_Borgman
Interaction between electrons, often complicating physical calculations
is influenced by the presence of all other electrons. Within the Hartree–Fock method of quantum chemistry, the antisymmetric wave function is approximated
Electronic_correlation
Surname list
process in plant metabolism Fock-Mehler transform, an integral transform introduced by Mehler (1881) and rediscovered by Fock (1943) Heine-Mehler formula
Mehler
Process in quantum computing
code as identical particles, mapping them to a single bosonic mode in the Fock basis, thereby linking qubit codes to bosonic codes. Constant-excitation
Quantum_error_correction
successful in describing the molecular systems, they still need a Hartree-Fock wavefunction to provide a valid starting point. The perturbation theories
Complete active space perturbation theory
Complete_active_space_perturbation_theory
Tall ship tour of US ports for the country's 250th anniversary (2026)
Gladan ( Sweden) ARC Gloria ( Colombia) Godspeed ( United States) Gorch Fock ( Germany) BAE Guayas ( Ecuador) Juan Bautista Cambiaso ( Dominican Republic)
Sail250
Ukrainian physicist (1904–1994)
lattice. In 1929, Ivanenko and Fock described the parallel displacement of spinors in curved space-time (the famous Ivanenko–Fock coefficients). Nobel laureate
Dmitri_Ivanenko
FOCK STATE
FOCK STATE
FOCK STATE
FOCK STATE
FOCK STATE
FOCK STATE
FOCK STATE
FOCK STATE
FOCK STATE