Tan's adiabatic sweep theorem from the variational theorem for the scattering length

It is shown that variation of the one-particle dispersion in a universal many-body system enables us to obtain Tan's adiabatic sweep theorem and its generalization. The derivation based on Hellmann-Feynman variational for scattering length suggested our previous paper [Cherny Shanenko, Phys. Rev. E 62, 1646 (2000)]. As an example, effects spinless bosons are considered. With help theorem, we mean kinetic interaction energies derive virial homogeneous trapped bosons. results can easily be generalized two-component fermions with interactions between opposite spins.