Why is nuclear recoil in the Mössbauer effect a quantum mechanical process? I was trying to understand Mössbauer effect, I picture that it is similar to a gun recoil after firing a bullet out of it's chamber to conserve momentum... so where is the quantum mechanics here? Is it because of the particle involves is quantum? 
 A: Classically, the recoil from an atom's decay can be thought of as giving an impulse to that particular atom.  Since this atom is in a crystal lattice, this initial impulse will cause each of the normal modes of the lattice to be excited with some amplitude.  (This amplitude may possibly be zero, depending on where the atom is in the lattice and the direction of the recoil.)
But the lattice vibrations are effectively decoupled simple harmonic oscillators, each with a frequency $\omega_i$.  So when we treat the lattice quantum-mechanically, the amplitude of each normal mode's excitations translates into a set of probabilities $\mathcal{P}(n_i)$ that each normal mode will be excited to an energy level $n_i \hbar \omega_i$.  In particular, there is a finite probability that this impulse will fail to excite any lattice vibrations at all.  In such a case, the entire lattice (rather than a single atom) recoils; and since the mass of the entire lattice is huge compared to a single atom, the effects of the recoil on the emitted gamma ray are negligible.
