### ASA 125th Meeting Ottawa 1993 May

## 2pPA10. Classical sound waves as a coherent superposition of phonons.

**Philip L. Marston
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*Dept. of Phys., Washington State Univ., Pullman, WA 99164
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It is generally recognized that single mode classical light waves can be
represented as a particular superposition of photon occupation number states
[R. J. Glauber, Phys. Rev. 131, 2766--2788 (1963)]. The analogous superposition
of phonons is examined for a chain of equal masses coupled only through
nearest-neighbor harmonic potentials. This relates phonons to classical normal
modes. While the resulting coherent phonon state may be implicit in the work of
others, it illustrates the quantum limitations on the normal mode amplitude
(xi). The expectation value <(xi)> oscillates harmonically but the oscillating
wave packet has a quantum spread of order ((dirac h)/(omega)M)[sup 1/2], where
M is the mass of the chain. This magnitude agrees with estimates by others on
the quantum limitation on the detection of classical vibrations. [Work
supported by ONR.]