1. ### Shyan

1,630
Phonons are said to be the result of the quantization of crystal waves.Let the function $u=u_0 e^{i(\vec{k}\cdot\vec{r}-\omega t)}$ describe such a wave. Is it right to say that if we assume u to be the quantum mechanical wave function of a particle, that particle is a phonon?
Thanks

2. ### Zarqon

238
The function u itself has nothing to do with quantization, it's just a general wave function. The quantization arises in situations when you have special boundry conditions that limit the actual values on ω or k, so that only certain frequencies for example are allowed. Now, if we look at one such allowed frequency mode (in the case this is quantized at all) , we can say that the smallest possible excitation is 1 phonon*.

* though note that the mode could be in a superposition of being excited and not excited, so on average it could have smaller excitation energy, but if you have a device that measures the phonon number of suc a mode, then it would always register integer values.

10