We were just taught about phonons in solid state physics class. Last year we did QM and now we are starting QFT as well.

Phonons are excitations of a condensed matter field. I thought that we would be using the Schrödinger equation (SE), but no. It is also nowhere in the syllabus. I read questions on this site about using the Schrödinger equation for quantum fields and many answers say that the SE describes particles without any spin, but the phonon is spin zero. Why can we not use the SE or normal (no relativity) QM and for phonons and if I'm wrong and you can, then how?