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87 relations: Algebra, Ammonia, Angular frequency, Angular momentum, Angular momentum operator, Argon, Atomic physics, Basis function, Benzene, Block matrix, Bohr magneton, Bohr radius, Bound state, Carbon, Central force, Classical mechanics, Closed-form expression, Commutator, Complete set of commuting observables, Coulomb's law, Cyclotron, Degenerate matter, Density of states, Dimension, Eigenfunction, Eigenvalues and eigenvectors, Energy level, Euclidean vector, Fine-structure constant, Generating set of a group, Good quantum number, Hamiltonian (quantum mechanics), Harmonic oscillator, Helium, Hilbert space, Hydrogen, Hydrogen atom, Irreducible representation, Landau quantization, Laplace–Runge–Lenz vector, Linear combination, Linear independence, Linear map, Linear subspace, Liquid helium, Magnetic moment, Mathematical model, Matrix similarity, MOSFET, Multiplet, ..., Multiplication table, Neon, Observable, Operator (physics), Orthonormal basis, Orthonormality, Parameter, Parity (physics), Particle, Perturbation theory, Perturbation theory (quantum mechanics), Principal quantum number, Quantum mechanics, Quantum number, Quantum state, Quantum statistical mechanics, Quantum system, Representation (mathematics), Scalar (physics), Schrödinger equation, Self-adjoint operator, Special unitary group, Spin (physics), Spin–orbit interaction, Stark effect, Subspace topology, Superlattice, Symmetry, Symmetry group, Symmetry operation, Tensor product, Three-dimensional space, Two-state quantum system, Unitary operator, Wave function, Xenon, Zeeman effect. Expand index (37 more) »
Algebra
Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.
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Ammonia
Ammonia is a compound of nitrogen and hydrogen with the formula NH3.
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Angular frequency
In physics, angular frequency ω (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate.
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Angular momentum
In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational equivalent of linear momentum.
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Angular momentum operator
In quantum mechanics, the angular momentum operator is one of several related operators analogous to classical angular momentum.
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Argon
Argon is a chemical element with symbol Ar and atomic number 18.
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Atomic physics
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus.
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Basis function
In mathematics, a basis function is an element of a particular basis for a function space.
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Benzene
Benzene is an important organic chemical compound with the chemical formula C6H6.
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Block matrix
In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices.
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Bohr magneton
In atomic physics, the Bohr magneton (symbol μB) is a physical constant and the natural unit for expressing the magnetic moment of an electron caused by either its orbital or spin angular momentum.
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Bohr radius
The Bohr radius (a0 or rBohr) is a physical constant, approximately equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state.
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Bound state
In quantum physics, a bound state is a special quantum state of a particle subject to a potential such that the particle has a tendency to remain localised in one or more regions of space.
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Carbon
Carbon (from carbo "coal") is a chemical element with symbol C and atomic number 6.
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Central force
In classical mechanics, a central force on an object is a force that is directed along the line joining the object and the origin: where \scriptstyle \vec is the force, F is a vector valued force function, F is a scalar valued force function, r is the position vector, ||r|| is its length, and \scriptstyle \hat.
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Classical mechanics
Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars and galaxies.
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Closed-form expression
In mathematics, a closed-form expression is a mathematical expression that can be evaluated in a finite number of operations.
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Commutator
In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative.
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Complete set of commuting observables
In quantum mechanics, a complete set of commuting observables (CSCO) is a set of commuting operators whose eigenvalues completely specify the state of a system.
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Coulomb's law
Coulomb's law, or Coulomb's inverse-square law, is a law of physics for quantifying the amount of force with which stationary electrically charged particles repel or attract each other.
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Cyclotron
A cyclotron is a type of particle accelerator invented by Ernest O. Lawrence in 1929-1930 at the University of California, Berkeley, and patented in 1932.
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Degenerate matter
Degenerate matter is a highly dense state of matter in which particles must occupy high states of kinetic energy in order to satisfy the Pauli exclusion principle.
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Density of states
In solid-state and condensed matter physics, the density of states (DOS) of a system describes the number of states per interval of energy at each energy level available to be occupied.
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Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
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Eigenfunction
In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function f in that space that, when acted upon by D, is only multiplied by some scaling factor called an eigenvalue.
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Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.
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Energy level
A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy.
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Euclidean vector
In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.
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Fine-structure constant
In physics, the fine-structure constant, also known as Sommerfeld's constant, commonly denoted (the Greek letter ''alpha''), is a fundamental physical constant characterizing the strength of the electromagnetic interaction between elementary charged particles.
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Generating set of a group
In abstract algebra, a generating set of a group is a subset such that every element of the group can be expressed as the combination (under the group operation) of finitely many elements of the subset and their inverses.
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Good quantum number
In quantum mechanics, given a particular Hamiltonian H and an operator O with corresponding eigenvalues and eigenvectors given by O|q_j\rangle.
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Hamiltonian (quantum mechanics)
In quantum mechanics, a Hamiltonian is an operator corresponding to the total energy of the system in most of the cases.
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Harmonic oscillator
In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x: where k is a positive constant.
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Helium
Helium (from lit) is a chemical element with symbol He and atomic number 2.
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Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.
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Hydrogen
Hydrogen is a chemical element with symbol H and atomic number 1.
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Hydrogen atom
A hydrogen atom is an atom of the chemical element hydrogen.
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Irreducible representation
In mathematics, specifically in the representation theory of groups and algebras, an irreducible representation (\rho, V) or irrep of an algebraic structure A is a nonzero representation that has no proper subrepresentation (\rho|_W,W), W \subset V closed under the action of \. Every finite-dimensional unitary representation on a Hermitian vector space V is the direct sum of irreducible representations.
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Landau quantization
Landau quantization in quantum mechanics is the quantization of the cyclotron orbits of charged particles in magnetic fields.
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Laplace–Runge–Lenz vector
In classical mechanics, the Laplace–Runge–Lenz vector (or simply the LRL vector) is a vector used chiefly to describe the shape and orientation of the orbit of one astronomical body around another, such as a planet revolving around a star.
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Linear combination
In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).
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Linear independence
In the theory of vector spaces, a set of vectors is said to be if one of the vectors in the set can be defined as a linear combination of the others; if no vector in the set can be written in this way, then the vectors are said to be.
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Linear map
In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.
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Linear subspace
In linear algebra and related fields of mathematics, a linear subspace, also known as a vector subspace, or, in the older literature, a linear manifold, is a vector space that is a subset of some other (higher-dimension) vector space.
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Liquid helium
At standard pressure, the chemical element helium exists in a liquid form only at the extremely low temperature of −270 °C (about 4 K or −452.2 °F).
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Magnetic moment
The magnetic moment is a quantity that represents the magnetic strength and orientation of a magnet or other object that produces a magnetic field.
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Mathematical model
A mathematical model is a description of a system using mathematical concepts and language.
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Matrix similarity
In linear algebra, two n-by-n matrices and are called similar if for some invertible n-by-n matrix.
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MOSFET
MOSFET showing gate (G), body (B), source (S) and drain (D) terminals. The gate is separated from the body by an insulating layer (white). surface-mount packages. Operating as switches, each of these components can sustain a blocking voltage of 120nbspvolts in the ''off'' state, and can conduct a continuous current of 30 amperes in the ''on'' state, dissipating up to about 100 watts and controlling a load of over 2000 watts. A matchstick is pictured for scale. A cross-section through an nMOSFET when the gate voltage ''V''GS is below the threshold for making a conductive channel; there is little or no conduction between the terminals drain and source; the switch is off. When the gate is more positive, it attracts electrons, inducing an ''n''-type conductive channel in the substrate below the oxide, which allows electrons to flow between the ''n''-doped terminals; the switch is on. Simulation result for formation of inversion channel (electron density) and attainment of threshold voltage (IV) in a nanowire MOSFET. Note that the threshold voltage for this device lies around 0.45 V The metal-oxide-semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET) is a type of field-effect transistor (FET), most commonly fabricated by the controlled oxidation of silicon.
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Multiplet
In representation theory, a multiplet refers to a representation of a mathematical structure.
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Multiplication table
In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system.
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Neon
Neon is a chemical element with symbol Ne and atomic number 10.
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Observable
In physics, an observable is a dynamic variable that can be measured.
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Operator (physics)
In physics, an operator is a function over a space of physical states to another space of physical states.
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Orthonormal basis
In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for V whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other.
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Orthonormality
In linear algebra, two vectors in an inner product space are orthonormal if they are orthogonal and unit vectors.
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Parameter
A parameter (from the Ancient Greek παρά, para: "beside", "subsidiary"; and μέτρον, metron: "measure"), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc.
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Parity (physics)
In quantum mechanics, a parity transformation (also called parity inversion) is the flip in the sign of one spatial coordinate.
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Particle
In the physical sciences, a particle (or corpuscule in older texts) is a small localized object to which can be ascribed several physical or chemical properties such as volume, density or mass.
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Perturbation theory
Perturbation theory comprises mathematical methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem.
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Perturbation theory (quantum mechanics)
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one.
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Principal quantum number
In quantum mechanics, the principal quantum number (symbolized n) is one of four quantum numbers which are assigned to all electrons in an atom to describe that electron's state.
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Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
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Quantum number
Quantum numbers describe values of conserved quantities in the dynamics of a quantum system.
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Quantum state
In quantum physics, quantum state refers to the state of an isolated quantum system.
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Quantum statistical mechanics
Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems.
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Quantum system
A quantum system is a portion of the whole Universe (environment or physical world) which is taken under consideration to make analysis or to study for quantum mechanics pertaining to the wave-particle duality in that system.
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Representation (mathematics)
In mathematics, representation is a very general relationship that expresses similarities between objects.
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Scalar (physics)
A scalar or scalar quantity in physics is a physical quantity that can be described by a single element of a number field such as a real number, often accompanied by units of measurement.
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Schrödinger equation
In quantum mechanics, the Schrödinger equation is a mathematical equation that describes the changes over time of a physical system in which quantum effects, such as wave–particle duality, are significant.
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Self-adjoint operator
In mathematics, a self-adjoint operator on a finite-dimensional complex vector space V with inner product \langle\cdot,\cdot\rangle is a linear map A (from V to itself) that is its own adjoint: \langle Av,w\rangle.
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Special unitary group
In mathematics, the special unitary group of degree, denoted, is the Lie group of unitary matrices with determinant 1.
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Spin (physics)
In quantum mechanics and particle physics, spin is an intrinsic form of angular momentum carried by elementary particles, composite particles (hadrons), and atomic nuclei.
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Spin–orbit interaction
In quantum physics, the spin–orbit interaction (also called spin–orbit effect or spin–orbit coupling) is a relativistic interaction of a particle's spin with its motion inside a potential.
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Stark effect
The Stark effect is the shifting and splitting of spectral lines of atoms and molecules due to presence of an external electric field.
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Subspace topology
In topology and related areas of mathematics, a subspace of a topological space X is a subset S of X which is equipped with a topology induced from that of X called the subspace topology (or the relative topology, or the induced topology, or the trace topology).
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Superlattice
A superlattice is a periodic structure of layers of two (or more) materials.
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Symmetry
Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance.
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Symmetry group
In group theory, the symmetry group of an object (image, signal, etc.) is the group of all transformations under which the object is invariant with composition as the group operation.
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Symmetry operation
In the context of molecular symmetry, a symmetry operation is a permutation of atoms such that the molecule or crystal is transformed into a state indistinguishable from the starting state.
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Tensor product
In mathematics, the tensor product of two vector spaces and (over the same field) is itself a vector space, together with an operation of bilinear composition, denoted by, from ordered pairs in the Cartesian product into, in a way that generalizes the outer product.
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Three-dimensional space
Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point).
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Two-state quantum system
In quantum mechanics, a two-state system (also known as a two-level system) is a quantum system that can exist in any quantum superposition of two independent (physically distinguishable) quantum states.
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Unitary operator
In functional analysis, a branch of mathematics, a unitary operator is a surjective bounded operator on a Hilbert space preserving the inner product.
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Wave function
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system.
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Xenon
Xenon is a chemical element with symbol Xe and atomic number 54.
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Zeeman effect
The Zeeman effect, named after the Dutch physicist Pieter Zeeman, is the effect of splitting a spectral line into several components in the presence of a static magnetic field.
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Degeneracy (quantum mechanics), Degenerate Orbital, Degenerate energy level, Degenerate orbital, Degenerate orbitals, Degenerated energy level, Quantum degeneracy.
References
[1] https://en.wikipedia.org/wiki/Degenerate_energy_levels
