The correspondence principle revisited

FEB 01, 1984

The usual textbook formulation of Bohr’s frequency correspondence principle does not apply to all periodic systems, and the limits

n→∞

and

h→0

are not universally equivalent.

DOI: 10.1063/1.2916084

Richard L. Liboff

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.

This article is only available in PDF format

References

1. W. Heitler, The Quantum Theory of Radiation, third ed., Oxford U.P., London (1954).
2. E. P. Wigner, Phys. Rev. 40, 749 (1932).https://doi.org/PHRVAO
3. W. Heisenberg, Phys. Rev. 33, 879 (1925).https://doi.org/PHRVAO
4. M. Planck, Vorlesungen über die Theorie der Wärmestrahlung, Barth, Leipzig, first ed. 1906, second ed. 1913.
Theory of Heat Radiation, Dover, New York (1959).
5. For historical discussion on these topics and extensive references, see M. Jammer, The Conceptual Development of Quantum Mechanics, McGraw‐Hill, New York (1966).
6. P. Eherenfest, Z. Phys. 45, 455 (1927).https://doi.org/ZEPYAA
7. L. D. Landau, E. M. Lifshitz, Statistical Physics, Addison‐Wesley, Reading, Mass. (1958).
8. 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).
9. R. L. Liboff, Fond. of Phys. 5, 271 (1975).
10. M. Czerny, Z. Phys. 34, 227 (1925).https://doi.org/ZEPYAA
11. R. L. Liboff, Int. J. Th. Phys. 18, 185 (1979).https://doi.org/IJTPBM
12. R. L. Liboff, Ann. de la Fond. L. deBroglie 5, 215 (1980).

More about the Authors

Richard L. Liboff. Cornell University, Ithaca, New York.