expanding atomic displacements in terms of all lattice wave modes?

zhanhai

I find the expression:

"In general, one can expand the atomic displacements in terms of all the lattice wave
modes (resembles a Fourier series expansion)"

at:
https://courses.cit.cornell.edu/ece4.../handout17.pdf

But I have not found the expression in any other literature. (In fact, some literature, like P.Y. Yu and M. Cardona: Fundamentals of Semiconductors, a long wavelength limitation seems to have been imposed.) Is the above-cited expression correct (in 3D lattice)?

Thank for your assistance.

DrDu

Yes, that's true. Should be explained in any book on solid state theory.

Dickfore

Have you ever done normal mode decomposition of a system of coupled oscillators? This is the same, except that the system is infinite, but periodic boundary conditions are imposed.