This source is showing that solving the Schrödinger equation for a triatmoic linear molecule yields the same formula for the rotationaI quantum states $BJ(J+1)$ as for dipoles.
For dipoles, the total rotational energy can be expressed as the total length of the molecule $R$ and a particle with reduced mass $\mu$ which makes it possible to express the coordinates in the Schrodinger equation specifically for only one particle with that reduced mass $\mu$.
I am clueless how the Schrödinger equation is solved for triatomic linear molecules because there are more variables that can not be reduced the same way. I would therefore expect to be seperate coordinates for each atom in the Schrodinger equation, as well as more than one bond length.
How is it derived and is it actually possible to do so?