Symmetries of Two Atoms with Contact Interactions in a Ring Trap

We consider an idealized model of ultracold atoms in a ring-shaped optical trap with s-wave and p-wave contact interactions. The relative dynamics for two interacting particles are mapped onto a single particle traveling on a ring disrupted by zero-range delta-function barriers and delta-prime barriers. We categorize the symmetry groups of these potentials and find the exact solutions for stationary states. By classifying the energy spectrum in terms of the irreducible representations of the symmetry groups, we reveal that there are additional symmetries “hidden” in contact interactions.