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In physics, a correspondence principle is any one of several premises or assertions about the relationship between classical and quantum mechanics.The physicist Niels Bohr coined the term in 1920 [1] during the early development of quantum theory; he used it to explain how quantized classical orbitals connect to quantum radiation. [2]
where p r is the radial momentum canonically conjugate to the coordinate q, which is the radial position, and T is one full orbital period. The integral is the action of action-angle coordinates. This condition, suggested by the correspondence principle, is the only one possible, since the quantum numbers are adiabatic invariants.
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.
A heuristic postulate called the correspondence principle was introduced to quantum theory by Niels Bohr: in effect it states that some kind of continuity argument should apply to the classical limit of quantum systems as the value of the Planck constant normalized by the action of these systems becomes very small.
Nevertheless, as explained in the introduction, for states that are highly localized in space, the expected position and momentum will approximately follow classical trajectories, which may be understood as an instance of the correspondence principle. Similarly, we can obtain the instantaneous change in the position expectation value.
According to the correspondence principle, in certain limits the quantum equations of states must approach Hamilton's equations of motion.The latter state the following relation between the generalized coordinate q (e.g. position) and the generalized momentum p: {˙ = = {,}; ˙ = = {,}.
In the philosophy of science, under the correspondence principle, a limiting case theory is an earlier theory which becomes incorporated into a later, usually broader theory; that is to say, the earlier (limiting case) theory proves to be a special or limited case of the later theory. Technically, a theory is said to be a limiting case of ...
The correspondence principle is a concept in quantum theory and relativity. Correspondence principle may also refer to: Correspondence principle (sociology), correspondence between social class and available education; In public finance, the principle that identifies the places where it is beneficial to provide public goods and services