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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]
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.
The constant is introduced so that the Hamiltonian is reduced to the classical Hamiltonian in cases where the quantum system can be approximated by a classical system; the ability to make such an approximation in certain limits is called the correspondence principle. The solution of this differential equation is given by
In special relativity, the rule that Wilczek called "Newton's Zeroth Law" breaks down: the mass of a composite object is not merely the sum of the masses of the individual pieces. [87]: 33 Newton's first law, inertial motion, remains true. A form of Newton's second law, that force is the rate of change of momentum, also holds, as does the ...
In 1913, Niels Bohr displayed rudiments of the later defined correspondence principle and used it to formulate a model of the hydrogen atom which explained its line spectrum. In the next few years Arnold Sommerfeld extended the quantum rule to arbitrary integrable systems making use of the principle of adiabatic invariance of the quantum ...
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: {˙ = = {,}; ˙ = = {,}.
D'Alembert's principle, also known as the Lagrange–d'Alembert principle, is a statement of the fundamental classical laws of motion. It is named after its discoverer, the French physicist and mathematician Jean le Rond d'Alembert , and Italian-French mathematician Joseph Louis Lagrange .
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.