

Integrable families of hardcore particles with unequal masses in a onedimensional harmonic trap

We show that the dynamics of particles in a onedimensional harmonic trap with hardcore interactions can be solvable for certain arrangements of unequal masses. For any number of particles, there exist two familiesofunequalmassparticlesthat haveintegrabledynamics,andthereareadditionalexceptionalcases for three, four, and five particles. The integrable mass families are classified by Coxeter reflection groups and the corresponding solutions are Betheansatzlike superpositions of hyperspherical harmonics in the relative hyperangular coordinates that are then restricted to sectors of fixed particle order. We also provide evidence for superintegrability of these Coxeter mass families and conjecture maximal superintegrability.