The correspondence principle addresses the connection between classical and quantum physics. The simple statement that quantum mechanics reduces to classical mechanics in the limit where the principal quantum number n approaches infinity, while found in many textbooks, is not true in general. In this article we will give special attention to the notion that the quantum frequency spectrum of a periodic system reduces to the classical spectrum in this limit. Two simple counter‐examples—a particle in a cubical box, and a rigid rotator—will show us that the classical result is not always recovered in the limit of large quantum numbers.
REFERENCES
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W. Heitler, The Quantum Theory of Radiation, third ed., Oxford U.P., London (1954).
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M. Planck, Vorlesungen über die Theorie der Wärmestrahlung, Barth, Leipzig, first ed. 1906, second ed. 1913.
Theory of Heat Radiation, Dover, New York (1959).
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For historical discussion on these topics and extensive references, see M. Jammer, The Conceptual Development of Quantum Mechanics, McGraw‐Hill, New York (1966).
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L. D. Landau, E. M. Lifshitz, Statistical Physics, Addison‐Wesley, Reading, Mass. (1958).
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Original works together with a concise review of early contributions to the correspondence principle are presented in B. L. Van der Waerden, Sources of Quantum Mechanics, Dover, New York (1967).
All of Bohr's papers on correspondence appear in L. Rosenfeld, ed., Niels Bohr, Collected Works, Volume 3, North‐Holland, New York (1976).
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© 1984 American Institute of Physics.
1984
American Institute of Physics
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