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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 ]
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: {˙ = = {,}; ˙ = = {,}.
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.
Uncertainty principle of Heisenberg, 1927. The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is a limit to the precision with which certain pairs of physical properties, such as position and momentum, can be simultaneously known. In other words, the ...
Some basic principles generally accepted as part of the interpretation include the following: [2] Quantum mechanics is intrinsically indeterministic. The correspondence principle : in the appropriate limit, quantum theory comes to resemble classical physics and reproduces the classical predictions.
It was the first example of quantum dynamics when Erwin Schrödinger derived it in 1926, while searching for solutions of the Schrödinger equation that satisfy the correspondence principle. [1] The quantum harmonic oscillator (and hence the coherent states) arise in the quantum theory of a wide range of physical systems. [ 2 ]
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.
In classical mechanics, a canonical transformation of phase space coordinates is one which preserves the structure of the Poisson brackets. The new variables x′, p′ have the same Poisson brackets with each other as the original variables x, p. Time evolution is a canonical transformation, since the phase space at any time is just as good a ...