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  2. Born rule - Wikipedia

    en.wikipedia.org/wiki/Born_rule

    The Born rule is a postulate of quantum mechanics that gives the probability that a measurement of a quantum system will yield a given result. In one commonly used application, it states that the probability density for finding a particle at a given position is proportional to the square of the amplitude of the system's wavefunction at that position.

  3. Measurement in quantum mechanics - Wikipedia

    en.wikipedia.org/wiki/Measurement_in_quantum...

    The formula for this calculation is known as the Born rule. For example, a quantum particle like an electron can be described by a quantum state that associates to each point in space a complex number called a probability amplitude. Applying the Born rule to these amplitudes gives the probabilities that the electron will be found in one region ...

  4. Cox's theorem - Wikipedia

    en.wikipedia.org/wiki/Cox's_theorem

    Cox's theorem, named after the physicist Richard Threlkeld Cox, is a derivation of the laws of probability theory from a certain set of postulates. [1] [2] This derivation justifies the so-called "logical" interpretation of probability, as the laws of probability derived by Cox's theorem are applicable to any proposition.

  5. List of equations in quantum mechanics - Wikipedia

    en.wikipedia.org/wiki/List_of_equations_in...

    Defining equation SI unit ... P = Probability that particle 1 has position r 1 in volume V 1 with spin s z1 and particle 2 has position r 2 in volume V 2 with spin s ...

  6. Statistical mechanics - Wikipedia

    en.wikipedia.org/wiki/Statistical_mechanics

    In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in the fields of physics, biology, [1] chemistry, neuroscience, [2] computer science, [3] [4] information theory [5] and ...

  7. Quantum mechanics - Wikipedia

    en.wikipedia.org/wiki/Quantum_mechanics

    The Schrödinger equation relates the collection of probability amplitudes that pertain to one moment of time to the collection of probability amplitudes that pertain to another. [ 7 ] : 67–87 One consequence of the mathematical rules of quantum mechanics is a tradeoff in predictability between measurable quantities.

  8. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    Bertrand's ballot theorem (probability theory, combinatorics) Bertrand's postulate (number theory) Besicovitch covering theorem (mathematical analysis) Betti's theorem ; Beurling–Lax theorem (Hardy spaces) Bézout's theorem (algebraic geometry) Bing metrization theorem (general topology) Bing's recognition theorem (geometric topology)

  9. Bayes' theorem - Wikipedia

    en.wikipedia.org/wiki/Bayes'_theorem

    Independently of Bayes, Pierre-Simon Laplace used conditional probability to formulate the relation of an updated posterior probability from a prior probability, given evidence. He reproduced and extended Bayes's results in 1774, apparently unaware of Bayes's work, in 1774, and summarized his results in Théorie analytique des probabilités (1812).