I have two questions regarding this topic.
I captured the part of the section I'm referring to. If I didn't my question would probably not make sense. My first question is to the second to last sentence above:
"Notice also that the center-of-mass position vector $R$ does not appear in the Hamiltonian at all, which, classically, is a reflection of the fact that the momentum of the center of mass is conserved because there are no external forces."
Could someone elaborate as to why having no external forces allows the center of mass to be conserved?
"...the center-of-mass wave function contributes only an overall phase to the system wave function and so has no effect on calculating probabilities of relative motion quantities."
What does he mean by an overall phase? How do I see this mathematically, that the center-of-mass wave function is an overall phase? What does it even mean, that it's "an overall phase"?