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81 relations: Angular frequency, Angular momentum, Bra–ket notation, C0-semigroup, Cartesian coordinate system, Charged particle, Chemical bond, Classical mechanics, Commutator, Complex conjugate, Complex number, Conservation law, Conservation of energy, Continuous functional calculus, Degrees of freedom (physics and chemistry), Del, Detailed balance, Dot product, Double bond, Eigenvalues and eigenvectors, Electric dipole moment, Electric field, Electric potential energy, Electromagnetism, Electrostatics, Energy, Expected value, Functional calculus, G-factor (physics), Gaussian units, Gyromagnetic ratio, Hamilton–Jacobi equation, Hamiltonian mechanics, Hilbert space, Holomorphic functional calculus, Homomorphism, Hooke's law, International System of Units, Kinetic energy, Laplace operator, Lieb–Thirring inequality, Linear algebra, Magnetic field, Many-body problem, Mass, Matrix exponential, Moment of inertia, Momentum, Momentum operator, Operator (mathematics), ..., Operator (physics), Orthonormal basis, Partial derivative, Particle in a box, Paul Dirac, Pauli matrices, Potential energy, Potential theory, Propagator, Quantum mechanics, Quantum state, Real number, Rigid rotor, Rotation operator (quantum mechanics), Scalar potential, Schrödinger equation, Self-adjoint operator, Simple harmonic motion, Solution of Schrödinger equation for a step potential, Spectrum (functional analysis), Spin-½, Stone's theorem on one-parameter unitary groups, Time evolution, Triple bond, Unbounded operator, Unitary matrix, Unitary operator, Vector potential, Wave function, Wavelength, William Rowan Hamilton. Expand index (31 more) »
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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Bra–ket notation
In quantum mechanics, bra–ket notation is a standard notation for describing quantum states.
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C0-semigroup
In mathematics, a C0-semigroup, also known as a strongly continuous one-parameter semigroup, is a generalization of the exponential function.
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Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
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Charged particle
In physics, a charged particle is a particle with an electric charge.
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Chemical bond
A chemical bond is a lasting attraction between atoms, ions or molecules that enables the formation of chemical compounds.
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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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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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Complex conjugate
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.
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Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
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Conservation law
In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves over time.
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Conservation of energy
In physics, the law of conservation of energy states that the total energy of an isolated system remains constant, it is said to be ''conserved'' over time.
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Continuous functional calculus
In mathematics, particularly in operator theory and C*-algebra theory, a continuous functional calculus is a functional calculus which allows the application of a continuous function to normal elements of a C*-algebra.
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Degrees of freedom (physics and chemistry)
In physics, a degree of freedom is an independent physical parameter in the formal description of the state of a physical system.
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Del
Del, or nabla, is an operator used in mathematics, in particular in vector calculus, as a vector differential operator, usually represented by the nabla symbol ∇.
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Detailed balance
The principle of detailed balance is formulated for kinetic systems which are decomposed into elementary processes (collisions, or steps, or elementary reactions): At equilibrium, each elementary process should be equilibrated by its reverse process.
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Dot product
In mathematics, the dot product or scalar productThe term scalar product is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space.
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Double bond
A double bond in chemistry is a chemical bond between two chemical elements involving four bonding electrons instead of the usual two.
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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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Electric dipole moment
The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity.
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Electric field
An electric field is a vector field surrounding an electric charge that exerts force on other charges, attracting or repelling them.
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Electric potential energy
Electric potential energy, or electrostatic potential energy, is a potential energy (measured in joules) that results from conservative Coulomb forces and is associated with the configuration of a particular set of point charges within a defined system.
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Electromagnetism
Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles.
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Electrostatics
Electrostatics is a branch of physics that studies electric charges at rest.
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Energy
In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object.
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Expected value
In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents.
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Functional calculus
In mathematics, a functional calculus is a theory allowing one to apply mathematical functions to mathematical operators.
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G-factor (physics)
A g-factor (also called g value or dimensionless magnetic moment) is a dimensionless quantity that characterizes the magnetic moment and gyromagnetic ratio of an atom, a particle or nucleus.
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Gaussian units
Gaussian units constitute a metric system of physical units.
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Gyromagnetic ratio
In physics, the gyromagnetic ratio (also sometimes known as the magnetogyric ratio in other disciplines) of a particle or system is the ratio of its magnetic moment to its angular momentum, and it is often denoted by the symbol γ, gamma.
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Hamilton–Jacobi equation
In mathematics, the Hamilton–Jacobi equation (HJE) is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations, and is a special case of the Hamilton–Jacobi–Bellman equation.
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Hamiltonian mechanics
Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics and predicts the same outcomes as non-Hamiltonian classical mechanics.
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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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Holomorphic functional calculus
In mathematics, holomorphic functional calculus is functional calculus with holomorphic functions.
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Homomorphism
In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces).
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Hooke's law
Hooke's law is a principle of physics that states that the force needed to extend or compress a spring by some distance scales linearly with respect to that distance.
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International System of Units
The International System of Units (SI, abbreviated from the French Système international (d'unités)) is the modern form of the metric system, and is the most widely used system of measurement.
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Kinetic energy
In physics, the kinetic energy of an object is the energy that it possesses due to its motion.
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Laplace operator
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space.
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Lieb–Thirring inequality
In mathematics and physics, Lieb–Thirring inequalities provide an upper bound on the sums of powers of the negative eigenvalues of a Schrödinger operator in terms of integrals of the potential.
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Linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.
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Magnetic field
A magnetic field is a vector field that describes the magnetic influence of electrical currents and magnetized materials.
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Many-body problem
The many-body problem is a general name for a vast category of physical problems pertaining to the properties of microscopic systems made of a large number of interacting particles.
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Mass
Mass is both a property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied.
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Matrix exponential
In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function.
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Moment of inertia
The moment of inertia, otherwise known as the angular mass or rotational inertia, of a rigid body is a tensor that determines the torque needed for a desired angular acceleration about a rotational axis; similar to how mass determines the force needed for a desired acceleration.
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Momentum
In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object.
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Momentum operator
In quantum mechanics, the momentum operator is an operator which maps the wave function in a Hilbert space representing a quantum state to another function.
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Operator (mathematics)
In mathematics, an operator is generally a mapping that acts on the elements of a space to produce other elements of the same space.
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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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Partial derivative
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).
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Particle in a box
In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes a particle free to move in a small space surrounded by impenetrable barriers.
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Paul Dirac
Paul Adrien Maurice Dirac (8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century.
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Pauli matrices
In mathematical physics and mathematics, the Pauli matrices are a set of three complex matrices which are Hermitian and unitary.
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Potential energy
In physics, potential energy is the energy possessed by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.
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Potential theory
In mathematics and mathematical physics, potential theory is the study of harmonic functions.
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Propagator
In quantum mechanics and quantum field theory, the propagator is a function that specifies the probability amplitude for a particle to travel from one place to another in a given time, or to travel with a certain energy and momentum.
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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 state
In quantum physics, quantum state refers to the state of an isolated quantum system.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Rigid rotor
The rigid rotor is a mechanical model that is used to explain rotating systems.
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Rotation operator (quantum mechanics)
This article concerns the rotation operator, as it appears in quantum mechanics.
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Scalar potential
Scalar potential, simply stated, describes the situation where the difference in the potential energies of an object in two different positions depends only on the positions, not upon the path taken by the object in traveling from one position to the other.
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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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Simple harmonic motion
In mechanics and physics, simple harmonic motion is a special type of periodic motion or oscillation motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement.
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Solution of Schrödinger equation for a step potential
In quantum mechanics and scattering theory, the one-dimensional step potential is an idealized system used to model incident, reflected and transmitted matter waves.
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Spectrum (functional analysis)
In mathematics, particularly in functional analysis, the spectrum of a bounded operator is a generalisation of the set of eigenvalues of a matrix.
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Spin-½
In quantum mechanics, spin is an intrinsic property of all elementary particles.
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Stone's theorem on one-parameter unitary groups
In mathematics, Stone's theorem on one-parameter unitary groups is a basic theorem of functional analysis that establishes a one-to-one correspondence between self-adjoint operators on a Hilbert space \mathcal and one-parameter families of unitary operators that are strongly continuous, i.e., and are homomorphisms, i.e., Such one-parameter families are ordinarily referred to as strongly continuous one-parameter unitary groups.
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Time evolution
Time evolution is the change of state brought about by the passage of time, applicable to systems with internal state (also called stateful systems).
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Triple bond
A triple bond in chemistry is a chemical bond between two atoms involving six bonding electrons instead of the usual two in a covalent single bond.
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Unbounded operator
In mathematics, more specifically functional analysis and operator theory, the notion of unbounded operator provides an abstract framework for dealing with differential operators, unbounded observables in quantum mechanics, and other cases.
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Unitary matrix
In mathematics, a complex square matrix is unitary if its conjugate transpose is also its inverse—that is, if where is the identity matrix.
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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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Vector potential
In vector calculus, a vector potential is a vector field whose curl is a given vector field.
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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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Wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
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William Rowan Hamilton
Sir William Rowan Hamilton MRIA (4 August 1805 – 2 September 1865) was an Irish mathematician who made important contributions to classical mechanics, optics, and algebra.
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Hamilton operator, Hamiltonian (quantum theory), Hamiltonian Operator, Hamiltonian operator, Kinetic energy operator, Quantum Hamiltonian, Schrödinger operator.
References
[1] https://en.wikipedia.org/wiki/Hamiltonian_(quantum_mechanics)
