Postprint version. Published in American Journal of Physics, Volume 70, Issue 3, March 1, 2002, pages 227-237.
NOTE: At the time of publication, the author Thomas Gutierrez was not yet affiliated with Cal Poly.
The definitive version is available at https://doi.org/10.1119/1.1446858.
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.
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