  We study representations of the Schr\"odinger algebra in terms of operators
in nonrelativistic conformal field theories. We prove a correspondence between
primary operators and eigenstates of few-body systems in a harmonic potential.
Using the correspondence we compute analytically the energy of fermions at
unitarity in a harmonic potential near two and four spatial dimensions. We also
compute the energy of anyons in a harmonic potential near the bosonic and
fermionic limits.
