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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]
Inertial motion is motion free of all forces. In Newtonian mechanics, the force F acting on a particle with mass m is given by Newton's second law, = ¨, where the acceleration is given by the second derivative of position r with respect to time t. Zero force means that inertial motion is just motion with zero acceleration:
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.
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 ...
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 1904 he expanded that principle by saying: "The principle of relativity, according to which the laws of physical phenomena must be the same for a stationary observer as for one carried along in a uniform motion of translation, so that we have no means, and can have none, of determining whether or not we are being carried along in such a motion."
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.
2: By its intrinsic force (alone) every body would progress uniformly in a straight line to infinity unless something external hinders that. (Newton's later first law of motion is to similar effect, Law 1 in the Principia.) 3: Forces combine by a parallelogram rule. Newton treats them in effect as we now treat vectors.