  Knowledge of the ground state of a homogeneous quantum many-body system can
be used to find the exact ground state of a dual inhomogeneous system with a
confining potential. For the complete family of parent Hamiltonians with a
ground state of Bijl-Jastrow form in free space, the dual system is shown to
include a one-body harmonic potential and two-body long-range interactions. The
extension to anharmonic potentials and quantum solids with Nosanov-Jastrow
wavefunctions is also presented. We apply this exact mapping to construct
eigenstates of trapped systems from free-space solutions with a variety of pair
correlation functions and interparticle interactions.
