The wave functions for the rigid rotator are often written as Y (\\ theta,\\ phi) instead of\\ psi since they can be seperated into a component that depends only on\\ theta and a component that depends only on\\ phi.
The wave functions for the rigid rotator, Y (\\ theta,\\ phi), can be separated a product of two functions. One of these functions depends only on\\ theta and the other depends only on\\ phi.