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.

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References

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More about the authors

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