# Clarification on inertial mass

I was talking to my friend the other day about the origin of inertia and it pondered both of our brains. I would like to know if the concept of inertia exists at the quantum level? I realize that quantized particles are probabilistic and cannot be understood at a classic level. So, does this mean inertia is applicable to only complicated systems like an atom and molecules, etc? There is such a huge gap in connection between classical and quantum systems it destroys my brain..

• "There is such a huge gap in connection between classical and quantum systems it destroys my brain.." made me laugh :D – Danu May 19 '15 at 20:41

Along another line, one can argue via the Ehrenfest theorem, that: $$m \partial_t^2 \langle x \rangle = -\langle \nabla V(x) \rangle$$ Therfore, the Newton axioms hold for the center of mass, if $V(x)$ scales on a scale much smaller than the wave packet (or $V$ is the harmonic oscillator potential, then $-\langle \nabla V(x) \rangle = - \langle kx \rangle = -k \langle x \rangle$). ($F = ma$ implies that the law on inertia holds).