As a counterpart to the quantum mechanical translation operator (see for example this post) is there a unitary operator which describes the stretching of a line. That is consider I have a chain of particles on a line, spaced at equal distances, $d$, from one another. The chain is assumed to be 1D and symmetric with respect to the origin.
I want to describe the transformation of this chain into another such that the equal separation distance is instead $2d$. This will correspond to a stretching of the whole line about the origin. Can a unitary, similar to that used to describe the translation of individial particles, be used to describe this?