Dynamics of Rigid Bodies (rotation, angular notions, etc) in quantum physics view

When I was studying the rotation of rigid bodies, I came to this notion of rigid body, and many other assumptions. However in the real world there is no rigid body. All bodies are composed of millions of particles interacting with each other. For example, if I push a certain part of a rod, the force propagates from the initial set of particles to the rest of the body, and millions of molecules are stretched. The body is deformed in a minuscular scale and lots of electrical forces are involved. I want to ask what actually happens between those particles to let the meta phenomena happens? Is there any theorem that can explain such an observation (propagation of force, interaction of molecules, etc) and to derivate the more familiar laws in rotation of rigid bodies such as the parallel axis theorem? Thanks for any ideas.

• The equations of quantum mechanics often contain a variable(s) that, when set to a given value, reproduces the classical world phenomenona that we measure. For a very old (and often misused) idea on this topic, the correspondence principle of Bohr is related. – user179430 Dec 31 '17 at 9:47

As for the parallel axis theorem, it describes how mass 'flows' around a rotation axis, the atoms away carrying more momentum than those near the center of rotation. The inertial moment describes the effective mass of a body in rotation. It is how the distribution of mass carries momentum $I_{moment}=\int{r^2 dm}$.