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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.
Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms. [2]: 1.1 It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot.
Quantum mechanics is intrinsically indeterministic. The correspondence principle: in the appropriate limit, quantum theory comes to resemble classical physics and reproduces the classical predictions. The Born rule: the wave function of a system yields probabilities for the outcomes of measurements upon that system.
The old quantum theory is a collection of results from the years 1900–1925 [23] which predate modern quantum mechanics. The theory was never complete or self-consistent, but was rather a set of heuristic corrections to classical mechanics. [24] The theory is now understood as a semi-classical approximation [25] to modern quantum mechanics. [26]
The definition of quantum theorists' terms, such as wave function and matrix mechanics, progressed through many stages.For instance, Erwin Schrödinger originally viewed the electron's wave function as its charge density smeared across space, but Max Born reinterpreted the absolute square value of the wave function as the electron's probability density distributed across space; [3]: 24–33 ...
Leonard I. Schiff (1968) Quantum Mechanics McGraw-Hill Education; Davydov A.S. (1965) Quantum Mechanics Pergamon ISBN 9781483172026; Shankar, Ramamurti (2011). Principles of Quantum Mechanics (2nd ed.). Plenum Press. ISBN 978-0306447907. von Neumann, John (2018). Nicholas A. Wheeler (ed.). Mathematical Foundations of Quantum Mechanics ...
In consequence, quantum theory is "a tighter package than one might have first thought". [24]: 94–95 Various approaches to rederiving the quantum formalism from alternative axioms have, accordingly, employed Gleason's theorem as a key step, bridging the gap between the structure of Hilbert space and the Born rule. [c]
Each point in the Bloch ball is a possible quantum state for a qubit.In QBism, all quantum states are representations of personal probabilities. In physics and the philosophy of physics, quantum Bayesianism is a collection of related approaches to the interpretation of quantum mechanics, the most prominent of which is QBism (pronounced "cubism").