Hyperspherical approach to dipolar droplets beyond the mean-field limit

We apply a hyperspherical formulation to a trapped Bose-Einstein condensate with dipolar and contact interactions. Central to this approach is a general correspondence between $K$-harmonic hyperspherical methods and a suitable Gaussian ansatz to the Gross-Pitaevskii equation, regardless of the form of the interparticle potential. This correspondence allows one to obtain hyperspherical potential energies for a wide variety of physical problems. In the case of the dipolar Bose-Einstein condensate, this motivates the inclusion of a beyond-mean-field term within the hyperspherical picture, which allows us to describe the energies and wave functions of excitations of self-bound dipolar droplets outside the mean-field limit.