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:''This article discusses quantum theory and relativity. For other uses, see Correspondence principle (disambiguation). In physics, the correspondence principle states that the behavior of systems described by the theory of quantum mechanics (or by the old quantum theory) reproduces classical physics in the limit of large quantum numbers. In other words, it says that for large orbits and for large energies, quantum calculations must agree with classical calculations. The principle was formulated by Niels Bohr in 1920,〔 (English translation in )〕 though he had previously made use of it as early as 1913 in developing his model of the atom.〔, Section 3.2〕 The term is also used more generally, to represent the idea that a new theory should reproduce the results of older well-established theories (which become limiting cases) in those domains where the old theories work. Classical quantities appear in quantum mechanics in the form of expected values of observables, and as such the Ehrenfest theorem (which predicts the time evolution of the expected values) lends support to the correspondence principle. ==Quantum mechanics== The rules of quantum mechanics are highly successful in describing microscopic objects, atoms and elementary particles. But ''macroscopic systems'', like springs and capacitors, are accurately described by classical theories like classical mechanics and classical electrodynamics. If quantum mechanics were to be applicable to macroscopic objects, there must be some limit in which quantum mechanics reduces to classical mechanics. ''Bohr's correspondence principle demands that classical physics and quantum physics give the same answer when the systems become large''.〔 〕 The conditions under which quantum and classical physics agree are referred to as the correspondence limit, or the classical limit. Bohr provided a rough prescription for the correspondence limit: it occurs ''when the quantum numbers describing the system are large''. A more elaborated analysis of quantum-classical correspondence (QCC) in wavepacket spreading leads to the distinction between robust "restricted QCC" and fragile "detailed QCC".〔 〕 "Restricted QCC" refers to the first two moments of the probability distribution and is true even when the wave packets diffract, while "detailed QCC" requires smooth potentials which vary over scales much larger than the wavelength, which is what Bohr considered. The post-1925 new quantum theory came in two different formulations. In matrix mechanics, the correspondence principle was built in and was used to construct the theory. In the Schrödinger approach classical behavior is not clear because the waves spread out as they move. Once the Schrödinger equation was given a probabilistic interpretation, Ehrenfest showed that Newton's laws hold on average: the quantum statistical expectation value of the position and momentum obey Newton's laws. The correspondence principle is one of the tools available to physicists for selecting quantum theories corresponding to reality. The principles of quantum mechanics are broad: states of a physical system form a complex vector space and physical observables are identified with Hermitian operators that act on this Hilbert space. The correspondence principle limits the choices to those that reproduce classical mechanics in the correspondence limit. Because quantum mechanics only reproduces classical mechanics in a statistical interpretation, and because the statistical interpretation only gives the probabilities of different classical outcomes, Bohr has argued that classical physics does not emerge from quantum physics in the same way that classical mechanics emerges as an approximation of special relativity at small velocities. He argued that classical physics exists independently of quantum theory and cannot be derived from it. His position is that it is inappropriate to understand the experiences of observers using purely quantum mechanical notions such as wavefunctions because the different states of experience of an observer are defined classically, and do not have a quantum mechanical analog. The relative state interpretation of quantum mechanics is an attempt to understand the experience of observers using only quantum mechanical notions. Niels Bohr was an early opponent of such interpretations. Many of these conceptual problems, however, resolve in the phase-space formulation of quantum mechanics, where the ''same variables with the same interpretation'' are utilized to describe both quantum and classical mechanics. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Correspondence principle」の詳細全文を読む スポンサード リンク
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