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112 relations: Absolute value, Albert Einstein, Almost surely, Argument (complex analysis), Atom (measure theory), Atomic emission spectroscopy, Born rule, Bra–ket notation, Commutator, Complex number, Conditional probability, Configuration space (physics), Continuity equation, Copenhagen interpretation, Countable set, Degenerate energy levels, Diagonal matrix, Dimension (vector space), Dimensional analysis, Direct product, Double-slit experiment, Eigenvalues and eigenvectors, Ensemble interpretation, Erwin Schrödinger, Free particle, Function space, Fundamental frequency, Hilbert space, Independence (probability theory), Indexed family, Inner product space, Integral, Interpretations of quantum mechanics, John Clive Ward, Lebesgue measure, Linear combination, M-theory, Manifold, Markov chain, Mass, Matrix element (physics), Matter wave, Max Born, Measurable function, Measurement in quantum mechanics, Motion (physics), Multiplication, Mutual exclusivity, Nobel Prize in Physics, Normed vector space, ..., Observable, One-dimensional space, Operator (physics), Orthonormal basis, Outer product, Particle in a box, Path integral formulation, Phase space formulation, Photon, Polarization (waves), Position and momentum space, Position operator, Potential energy, Probability, Probability axioms, Probability current, Probability density function, Probability distribution, Probability measure, Product measure, Projective Hilbert space, Quantum entanglement, Quantum eraser experiment, Quantum field theory, Quantum harmonic oscillator, Quantum mechanics, Quantum state, Quantum superposition, Quantum system, Radon–Nikodym theorem, Real line, Real number, Real-valued function, Rectangular potential barrier, Richard Feynman, Row and column vectors, S-matrix, Scattering theory, Schrödinger equation, Series (mathematics), Smoothness, Spectral theory, Spherical harmonics, Square (algebra), Square-integrable function, Standard basis, Statistical ensemble (mathematical physics), Summation, The Feynman Lectures on Physics, Three-dimensional space, Time evolution, Two-state quantum system, Uncertainty principle, Unit vector, Unitary matrix, Unitary operator, Vector space, Wave function, Wave function collapse, Wave interference, Wave packet, Weight function. Expand index (62 more) »
Absolute value
In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.
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Albert Einstein
Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist who developed the theory of relativity, one of the two pillars of modern physics (alongside quantum mechanics).
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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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Argument (complex analysis)
In mathematics, the argument is a multi-valued function operating on the nonzero complex numbers.
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Atom (measure theory)
In mathematics, more precisely in measure theory, an atom is a measurable set which has positive measure and contains no set of smaller positive measure.
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Atomic emission spectroscopy
Atomic emission spectroscopy (AES) is a method of chemical analysis that uses the intensity of light emitted from a flame, plasma, arc, or spark at a particular wavelength to determine the quantity of an element in a sample.
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Born rule
The Born rule (also called the Born law, Born's rule, or Born's law) formulated by German physicist Max Born in 1926, is a law of quantum mechanics giving the probability that a measurement on a quantum system will yield a given result.
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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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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 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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Conditional probability
In probability theory, conditional probability is a measure of the probability of an event (some particular situation occurring) given that (by assumption, presumption, assertion or evidence) another event has occurred.
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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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Continuity equation
A continuity equation in physics is an equation that describes the transport of some quantity.
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Copenhagen interpretation
The Copenhagen interpretation is an expression of the meaning of quantum mechanics that was largely devised in the years 1925 to 1927 by Niels Bohr and Werner Heisenberg.
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Countable set
In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.
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Degenerate energy levels
In quantum mechanics, an energy level is degenerate if it corresponds to two or more different measurable states of a quantum system.
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Diagonal matrix
In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero.
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Dimension (vector space)
In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V over its base field.
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Dimensional analysis
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric charge) and units of measure (such as miles vs. kilometers, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed.
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Direct product
In mathematics, one can often define a direct product of objects already known, giving a new one.
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Double-slit experiment
In modern physics, the double-slit experiment is a demonstration that light and matter can display characteristics of both classically defined waves and particles; moreover, it displays the fundamentally probabilistic nature of quantum mechanical phenomena.
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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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Ensemble interpretation
The ensemble interpretation of quantum mechanics considers the quantum state description to apply only to an ensemble of similarly prepared systems, rather than supposing that it exhaustively represents an individual physical system.
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Erwin Schrödinger
Erwin Rudolf Josef Alexander Schrödinger (12 August 1887 – 4 January 1961), sometimes written as or, was a Nobel Prize-winning Austrian physicist who developed a number of fundamental results in the field of quantum theory, which formed the basis of wave mechanics: he formulated the wave equation (stationary and time-dependent Schrödinger equation) and revealed the identity of his development of the formalism and matrix mechanics.
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Free particle
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 varies.
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Function space
In mathematics, a function space is a set of functions between two fixed sets.
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Fundamental frequency
The fundamental frequency, often referred to simply as the fundamental, is defined as the lowest frequency of a periodic waveform.
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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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Independence (probability theory)
In probability theory, two events are independent, statistically independent, or stochastically independent if the occurrence of one does not affect the probability of occurrence of the other.
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Indexed family
In mathematics, an indexed family is informally a collection of objects, each associated with an index from some index set.
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Inner product space
In linear algebra, an inner product space is a vector space with an additional structure called an inner product.
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Integral
In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.
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Interpretations of quantum mechanics
An interpretation of quantum mechanics is an attempt to explain how concepts in quantum mechanics correspond to reality.
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John Clive Ward
John Clive Ward, (1 August 1924 – 6 May 2000) was a British-Australian physicist.
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Lebesgue measure
In measure theory, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of n-dimensional Euclidean space.
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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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M-theory
M-theory is a theory in physics that unifies all consistent versions of superstring theory.
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Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
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Markov chain
A Markov chain is "a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event".
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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 element (physics)
In physics, particularly in quantum perturbation theory, the "matrix element" refers to the linear operator of a modified Hamiltonian using Dirac notation.
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Matter wave
Matter waves are a central part of the theory of quantum mechanics, being an example of wave–particle duality.
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Max Born
Max Born (11 December 1882 – 5 January 1970) was a German physicist and mathematician who was instrumental in the development of quantum mechanics.
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Measurable function
In mathematics and in particular measure theory, a measurable function is a function between two measurable spaces such that the preimage of any measurable set is measurable, analogously to the definition that a function between topological spaces is continuous if the preimage of each open set is open.
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Measurement in quantum mechanics
The framework of quantum mechanics requires a careful definition of measurement.
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Motion (physics)
In physics, motion is a change in position of an object over time.
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Multiplication
Multiplication (often denoted by the cross symbol "×", by a point "⋅", by juxtaposition, or, on computers, by an asterisk "∗") is one of the four elementary mathematical operations of arithmetic; with the others being addition, subtraction and division.
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Mutual exclusivity
In logic and probability theory, two events (or propositions) are mutually exclusive or disjoint if they cannot both occur (be true).
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Nobel Prize in Physics
The Nobel Prize in Physics (Nobelpriset i fysik) is a yearly award given by the Royal Swedish Academy of Sciences for those who conferred the most outstanding contributions for mankind in the field of physics.
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Normed vector space
In mathematics, a normed vector space is a vector space over the real or complex numbers, on which a norm is defined.
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Observable
In physics, an observable is a dynamic variable that can be measured.
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One-dimensional space
In physics and mathematics, a sequence of n numbers can specify a location in n-dimensional 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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Outer product
In linear algebra, an outer product is the tensor product of two coordinate vectors, a special case of the Kronecker product of matrices.
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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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Path integral formulation
The path integral formulation of quantum mechanics is a description of quantum theory that generalizes the action principle of classical mechanics.
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Phase space formulation
The phase space formulation of quantum mechanics places the position and momentum variables on equal footing, in phase space.
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Photon
The photon is a type of elementary particle, the quantum of the electromagnetic field including electromagnetic radiation such as light, and the force carrier for the electromagnetic force (even when static via virtual particles).
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Polarization (waves)
Polarization (also polarisation) is a property applying to transverse waves that specifies the geometrical orientation of the oscillations.
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Position and momentum space
In physics and geometry, there are two closely related vector spaces, usually three-dimensional but in general could be any finite number of dimensions.
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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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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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Probability
Probability is the measure of the likelihood that an event will occur.
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Probability axioms
In Kolmogorov's probability theory, the probability P of some event E, denoted P(E), is usually defined such that P satisfies the Kolmogorov axioms, named after the Russian mathematician Andrey Kolmogorov, which are described below.
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Probability current
In quantum mechanics, the probability current (sometimes called probability flux) is a mathematical quantity describing the flow of probability in terms of probability per unit time per unit area.
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Probability density function
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function, whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.
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Probability distribution
In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.
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Probability measure
In mathematics, a probability measure is a real-valued function defined on a set of events in a probability space that satisfies measure properties such as countable additivity.
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Product measure
In mathematics, given two measurable spaces and measures on them, one can obtain a product measurable space and a product measure on that space.
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Projective Hilbert space
In mathematics and the foundations of quantum mechanics, the projective Hilbert space P(H) of a complex Hilbert space H is the set of equivalence classes of vectors v in H, with v \ne 0, for the relation \sim given by The equivalence classes for the relation \sim are also called rays or projective rays.
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Quantum entanglement
Quantum entanglement is a physical phenomenon which occurs when pairs or groups of particles are generated, interact, or share spatial proximity in ways such that the quantum state of each particle cannot be described independently of the state of the other(s), even when the particles are separated by a large distance—instead, a quantum state must be described for the system as a whole.
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Quantum eraser experiment
In quantum mechanics, the quantum eraser experiment is an interferometer experiment that demonstrates several fundamental aspects of quantum mechanics, including quantum entanglement and complementarity.
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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 harmonic oscillator
The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator.
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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 superposition
Quantum superposition is a fundamental principle of quantum mechanics.
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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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Radon–Nikodym theorem
In mathematics, the Radon–Nikodym theorem is a result in measure theory.
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Real line
In mathematics, the real line, or real number line is the line whose points are the real numbers.
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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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Real-valued function
In mathematics, a real-valued function is a function whose values are real numbers.
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Rectangular potential barrier
In quantum mechanics, the rectangular (or, at times, square) potential barrier is a standard one-dimensional problem that demonstrates the phenomena of wave-mechanical tunneling (also called "quantum tunneling") and wave-mechanical reflection.
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Richard Feynman
Richard Phillips Feynman (May 11, 1918 – February 15, 1988) was an American theoretical physicist, known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics for which he proposed the parton model.
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Row and column vectors
In linear algebra, a column vector or column matrix is an m × 1 matrix, that is, a matrix consisting of a single column of m elements, Similarly, a row vector or row matrix is a 1 × m matrix, that is, a matrix consisting of a single row of m elements Throughout, boldface is used for the row and column vectors.
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S-matrix
In physics, the S-matrix or scattering matrix relates the initial state and the final state of a physical system undergoing a scattering process.
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Scattering theory
In mathematics and physics, scattering theory is a framework for studying and understanding the scattering of waves and particles.
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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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Series (mathematics)
In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.
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Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
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Spectral theory
In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces.
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Spherical harmonics
In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere.
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Square (algebra)
In mathematics, a square is the result of multiplying a number by itself.
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Square-integrable function
In mathematics, a square-integrable function, also called a quadratically integrable function, is a real- or complex-valued measurable function for which the integral of the square of the absolute value is finite.
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Standard basis
In mathematics, the standard basis (also called natural basis) for a Euclidean space is the set of unit vectors pointing in the direction of the axes of a Cartesian coordinate system.
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Statistical ensemble (mathematical physics)
In mathematical physics, especially as introduced into statistical mechanics and thermodynamics by J. Willard Gibbs in 1902, an ensemble (also statistical ensemble) is an idealization consisting of a large number of virtual copies (sometimes infinitely many) of a system, considered all at once, each of which represents a possible state that the real system might be in.
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Summation
In mathematics, summation (capital Greek sigma symbol: ∑) is the addition of a sequence of numbers; the result is their sum or total.
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The Feynman Lectures on Physics
The Feynman Lectures on Physics is a physics textbook based on some lectures by Richard P. Feynman, a Nobel laureate who has sometimes been called "The Great Explainer".
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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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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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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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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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Unit vector
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.
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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 space
A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
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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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Wave function collapse
In quantum mechanics, wave function collapse is said to occur when a wave function—initially in a superposition of several eigenstates—appears to reduce to a single eigenstate (by "observation").
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Wave interference
In physics, interference is a phenomenon in which two waves superpose to form a resultant wave of greater, lower, or the same amplitude.
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Wave packet
In physics, a wave packet (or wave train) is a short "burst" or "envelope" of localized wave action that travels as a unit.
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Weight function
A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set.
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Redirects here:
Born probability, Complex probability amplitude, Complex-valued probability amplitude, Quantum amplitude, Transition amplitude.
References
[1] https://en.wikipedia.org/wiki/Probability_amplitude
