Inequality Relating the Ground-State Energies of Two and Three Bosons

We report sufficient conditions for the validity of the inequality $E_0\mathrm{}\left(3\right)\mathrm{}\le 3E_0\mathrm{}\left(2\right)\mathrm{}$ for the ground-state energies of two and three nonrelativistic identical bosons interacting via spherically symmetric pair potentials.