Virial theorems for trapped cold atoms

We present a general virial theorem for quantum particles with arbitrary zero-range or finite-range interactions in an arbitrary external potential. We deduce virial theorems for several situations relevant to trapped cold atoms: zero-range interactions with and without Efimov effect, hard spheres, narrow Feshbach resonances, and finite-range interactions. If the scattering length a is varied adiabatically in a two-component Fermi gas, we find that the trapping potential energy as a function of 1/a has an inflexion point at unitarity.