A more elaborated analysis of quantum-classical correspondence (QCC) in wavepacket spreading leads to the distinction between robust "restricted QCC" and fragile "detailed QCC". Bohr provided a rough prescription for the correspondence limit: it occurs when the quantum numbers describing the system are large. The conditions under which quantum and classical physics agree are referred to as the correspondence limit, or the classical limit. Arnold Sommerfeld referred to the principle as "Bohrs Zauberstab" (Bohr's magic wand) in 1921. Bohr's correspondence principle demands that classical physics and quantum physics give the same answer when the systems become large. If quantum mechanics were to be applicable to macroscopic objects, there must be some limit in which quantum mechanics reduces to classical mechanics. But macroscopic systems, like springs and capacitors, are accurately described by classical theories like classical mechanics and classical electrodynamics. The rules of quantum mechanics are highly successful in describing microscopic objects, atoms and elementary particles. This concept is somewhat different from the requirement of a formal limit under which the new theory reduces to the older, thanks to the existence of a deformation parameter.Ĭlassical 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. The term codifies the idea that a new theory should reproduce under some conditions the results of older well-established theories in those domains where the old theories work. The principle was formulated by Niels Bohr in 1920, though he had previously made use of it as early as 1913 in developing his model of the atom. In other words, it says that for large orbits and for large energies, quantum calculations must agree with classical calculations. Thus Bohr's correspondence principle is established.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. Calculations show that for quantum number number n as large as 10000, the difference in v and f is less than 0.015%. Lim i t n → ∞=(Clasical Physics)įor example, quantum condition for emission of radiation is h v = E i − E fĪnd Maxwell's classical theory says that an electron revolving with orbital frequency f must radiate light waves of frequency f. We may thereofore rewrite Bohr's correspondence principle as: However, the probability of finding the electron is high near the Bohr orbit radius, and at the same time, the probability of finding the electron between these orbits is not zero.Īccording to Bohr's correspondence principle, the predictions of quantum theory must corresponds to the predictions of classical theory in the regions of sizes where classical theory must corresponds to the predictions of classical theory in the regions of sizes where classical theory holds.įor large size wherein classical theory holds good, quantum number n becomes large. According to this model, electrons in an atom do not move around the nucleus in definite orbits. As is know, Bohr's atom model has been replaced by quantum machanical model.
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