A unitary quantum gas in a harmonic trap: exact mapping to free space zero energy eigenstates and application to the three-body problem
Résumé
For a gas of particles interacting with a zero range potential of infinite scattering length, we show that the N-body eigenstates in an isotropic harmonic trap can be exactly expressed in terms of the zero energy untrapped eigenstates. This reduces the trapped case to the free space one. As first applications of this mapping, we calculate moments of the trapping pot ential energy, and the exact spectrum and eigenstates for three trapped identical particles.