The few-body problem for trapped bosons with large scattering length

We calculate energy levels of two and three bosons trapped in a harmonic oscillator potential with oscillator length $a_{\mathrm{o}sc}$. The atoms are assumed to interact through a short-range potential with a scattering length $a$, and the short-distance behavior of the three-body wave function is characterized by a parameter $\theta$. For large positive $a\mathrm{/}{a}_{\mathrm{o}sc}$, the energies of states which, in the absence of the trap, correspond to three free atoms approach values independent of $a$ and $\theta$. For other states the $\theta$ dependence of the energy is strong, but the energy is independent of $a$ for $\mathrm{\mid }a\mathrm{/}{a}_{\mathrm{o}sc}\mathrm{\mid }\gg 1$.