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Expectation value (quantum mechanics)

Index Expectation value (quantum mechanics)

In quantum mechanics, the expectation value is the probabilistic expected value of the result (measurement) of an experiment. [1]

35 relations: Almost surely, Arithmetic mean, Bra–ket notation, C*-algebra, Complex number, Configuration space (physics), Continuous spectrum, Density matrix, Domain of a function, Dynamics (mechanics), Eigenvalues and eigenvectors, Expected value, Heisenberg picture, Hilbert space, KMS state, Linear form, Momentum operator, Observable, Operator (physics), Position operator, Projection (linear algebra), Quantum field theory, Quantum mechanics, Quantum state, Quantum statistical mechanics, Schrödinger picture, Self-adjoint, Spectral theorem, Thermodynamics, Trace class, Ultraweak topology, Unbounded operator, Uncertainty principle, Virial theorem, Wave function.

Almost surely

In probability theory, one says that an event happens almost surely (sometimes abbreviated as a.s.) if it happens with probability one.

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Arithmetic mean

In mathematics and statistics, the arithmetic mean (stress on third syllable of "arithmetic"), or simply the mean or average when the context is clear, is the sum of a collection of numbers divided by the number of numbers in the collection.

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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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C*-algebra

C∗-algebras (pronounced "C-star") are an area of research in functional analysis, a branch of mathematics.

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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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Configuration space (physics)

In classical mechanics, the parameters that define the configuration of a system are called generalized coordinates, and the vector space defined by these coordinates is called the configuration space of the physical system.

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Continuous spectrum

In physics, a continuous spectrum usually means a set of attainable values for some physical quantity (such as energy or wavelength) that is best described as an interval of real numbers, as opposed to a discrete spectrum, a set of attainable values that is discrete in the mathematical sense, where there is a positive gap between each value and the next one.

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Density matrix

A density matrix is a matrix that describes a quantum system in a mixed state, a statistical ensemble of several quantum states.

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Domain of a function

In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.

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Dynamics (mechanics)

Dynamics is the branch of applied mathematics (specifically classical mechanics) concerned with the study of forces and torques and their effect on motion, as opposed to kinematics, which studies the motion of objects without reference to these forces.

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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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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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Heisenberg picture

In physics, the Heisenberg picture (also called the Heisenberg representation) is a formulation (largely due to Werner Heisenberg in 1925) of quantum mechanics in which the operators (observables and others) incorporate a dependency on time, but the state vectors are time-independent, an arbitrary fixed basis rigidly underlying the theory.

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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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KMS state

In the statistical mechanics of quantum mechanical systems and quantum field theory, the properties of a system in thermal equilibrium can be described by a mathematical object called a Kubo–Martin–Schwinger state or, more commonly, a KMS state: a state satisfying the KMS condition.

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Linear form

In linear algebra, a linear functional or linear form (also called a one-form or covector) is a linear map from a vector space to its field of scalars.

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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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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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Position operator

In quantum mechanics, the position operator is the operator that corresponds to the position observable of a particle.

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Projection (linear algebra)

In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.

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Quantum field theory

In theoretical physics, quantum field theory (QFT) is the theoretical framework for constructing quantum mechanical models of subatomic particles in particle physics and quasiparticles in condensed matter physics.

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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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Quantum statistical mechanics

Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems.

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Schrödinger picture

In physics, the Schrödinger picture (also called the Schrödinger representation) is a formulation of quantum mechanics in which the state vectors evolve in time, but the operators (observables and others) are constant with respect to time.

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Self-adjoint

In mathematics, an element x of a *-algebra is self-adjoint if x^*.

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Spectral theorem

In mathematics, particularly linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented as a diagonal matrix in some basis).

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Thermodynamics

Thermodynamics is the branch of physics concerned with heat and temperature and their relation to energy and work.

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Trace class

In mathematics, a trace class operator is a compact operator for which a trace may be defined, such that the trace is finite and independent of the choice of basis.

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Ultraweak topology

In functional analysis, a branch of mathematics, the ultraweak topology, also called the weak-* topology, or weak-* operator topology or σ-weak topology, on the set B(H) of bounded operators on a Hilbert space is the weak-* topology obtained from the predual B*(H) of B(H), the trace class operators on H. In other words it is the weakest topology such that all elements of the predual are continuous (when considered as functions on B(H)).

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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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Uncertainty principle

In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known.

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Virial theorem

In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy, \left\langle T \right\rangle, of a stable system consisting of N particles, bound by potential forces, with that of the total potential energy, \left\langle V_\text \right\rangle, where angle brackets represent the average over time of the enclosed quantity.

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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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Expectation value (quantum physics).

References

[1] https://en.wikipedia.org/wiki/Expectation_value_(quantum_mechanics)

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