correspondence principle

correspondence principle, physical principle, enunciated by Niels Bohr in 1923, according to which the predictions of the quantum theory must correspond to the predictions of the classical theories of physics when the quantum theory is used to describe the behavior of systems that can be successfully described by classical theories. Technically this principle means that the results of a quantum theory analysis of a problem that involves the use of very large quantum numbers must agree with the results of a classical physics analysis. Such correspondence is known as the classical limit of the quantum theory. Ordinarily the quantum theory is used to describe the behavior of bodies that are so small that they cannot be seen under an optical microscope, while the theories of classical physics are used to analyze the behavior of large-scale bodies. The correspondence principle provided an important theoretical basis for the development of a detailed correlation between the newer quantum theory and the classical physics that preceded it.

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correspondence principle [‚kär·ə′spän·dəns ‚prin·sə·pəl]

(quantum mechanics)

The principle that quantum mechanics has a classical limit in which it is equivalent to classical mechanics. Also known as Bohr's correspondence principle.

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Correspondence principle

A fundamental hypothesis according to which classical mechanics can be understood as a limiting case of quantum mechanics; or conversely, many characteristic features in quantum mechanics can be approximated on the basis of classical mechanics, provided classical mechanics is properly reinterpreted. This idea was first proposed by N. Bohr in the early 1920s as a set of rules for understanding the spectra of simple atoms and molecules.

The classical motions in simple dynamical systems can be understood as composed of independent partial motions, each with its own degree of freedom. Each degree of freedom accumulates its own classical action-integral. The frequency of the classical motion for any particular degree of freedom is given by the partial derivative of the energy function with respect to the corresponding action. Bohr noticed that this classical result yields the correct quantum-theoretical result for the light frequency in a transition from one energy level to another, provided the derivative is replaced by the difference in the energies. Moreover, precise information about the possibility of such transitions and their intensities is obtained by analyzing the related classical motion. This information becomes better as the quantum numbers involved be come larger. The apparent inconsistencies in Bohr's quantum theory are thereby overcome by a set of rules that came to be called the correspondence principle. See Action

After 1925, the success of the new quantum mechanics, particularly wave mechanics, reduced the correspondence principle to a somewhat vague article of faith among physicists. However, the appeal to classical mechanics is still convenient for some rather crude estimates such as the total number of levels below a given energy. Such estimates help in finding the approximate shape of large atoms and large nuclei in the Thomas-Fermi model.

The correspondence principle, however, has assumed a more profound significance. Experimental techniques in atomic, molecular, mesoscopic, and nuclear physics have improved dramatically. High-precision data for many thousands of energy levels are available where the traditional methods of quantum mechanics are not very useful or informative. However, the basic idea behind the correspondence principle must still be valid: Quantum mechanics must be understandable in terms of classical mechanics for the highly excited states, even in difficult cases like the three-body problem, where the overall behavior seems unpredictable and chaotic. The wider application of Bohr's correspondence principle allows many basic but difficult problems to be seen in a new light. See Atomic structure and spectra, Chaos, Mesoscopic physics, Molecular structure and spectra, Quantum mechanics