For me this question becomes really apparent when we make a transformation e.g. in a H-atom from the proton frame of reference to the electron frame of reference. The whole point of QM is that the electron cannot be treated as a dot somewhere in space but that it has an associated wavefunction and only acquires a certain position when I make an appropriate measurement. So how can I transform to the electron frame of reference making the origin to be the position of the electron if I don't know it?
In a wider sense how can I define a coordinate system in quantum mechanics? The usual "take a corner of the lab as the origin and the edges of the walls as axes" surely doesn't work because these all consist of particles that don't have well-defined positions.