Postprint version. Published in American Journal of Physics, Volume 70, Issue 3, March 1, 2002, pages 227-237.
Copyright © 2002 American Association of Physics Teachers. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Association of Physics Teachers. The following article appeared in American Journal of Physics and may be found at http://dx.doi.org/10.1119/1.1446858.
NOTE: At the time of publication, the author Thomas Gutierrez was not yet affiliated with Cal Poly.
A phonon often is described as ‘‘a quantum of lattice vibration,’’ but this description can be difficult to reconcile with the wave functions explored in a typical undergraduate quantum mechanics class. A phonon wave function is similar to the harmonic oscillator wave functions studied in introductory quantum mechanics, except that it is many-dimensional. We suggest a way to visualize the probability density for this very high-dimensional wave function. The resulting pictures are especially clear and intuitive for a coherent state, which is both a good approximation to a sound wave and a discrete analog to laser light. These pictures can also provide a qualitative introduction to quantum field theory.