ASA 125th Meeting Ottawa 1993 May

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

Philip L. Marston

Dept. of Phys., Washington State Univ., Pullman, WA 99164

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.]