In my lectures on quantum mechanics, it was said that the Hamiltonian for a hydrogenic atom could be split into relative motion and translational motion, as follows:
$$\hat{H} = - \frac{\hbar^2}{2m}\nabla^2_{cm} - \frac{\hbar^2}{2\mu}\nabla^2 - \frac{Ze^2}{4\pi\epsilon_0r}$$
and that one only need consider the relative motion:
$$\hat{H} = - \frac{\hbar^2}{2\mu}\nabla^2 - \frac{Ze^2}{4\pi\epsilon_0r}$$
This statement is reiterated in Atkins' Physical Chemistry (10th Edition), as well as his Molecular Quantum Mechanics (4th Edition), and various other online resources, but I am yet to find an explanation as to why.
Why can we, and why do we, neglect the translational motion of the atom?