  We study Schr\"odinger invariant field theories (nonrelativistic conformal
field theories) in the large charge (particle number) sector. We do so by
constructing the effective field theory (EFT) for a Goldstone boson of the
associated $U(1)$ symmetry in a harmonic potential. This EFT can be studied
semi-classically in a large charge expansion. We calculate the dimensions of
the lowest lying operators, as well as correlation functions of charged
operators. We find universal behavior of three point function in large charge
sector. We comment on potential applications to fermions at unitarity and
critical anyon systems.
