Dimer problem on a spherical surface

We solve the problem of a dimer moving on a spherical surface and find that its binding energy and wave function are sensitive to the total angular momentum. The dimer gets squeezed in the direction orthogonal to the center-of-mass motion and can qualitatively change its geometry from two-dimensional to one-dimensional. These results suggest that combining the curved geometry with finite angular momentum may give rise to qualitatively new many-body phenomena in ultracold shell-shaped gases.