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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 $a_{\mathrm osc}$. 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 $θ$. For large positive $a/a_{\mathrm osc}$, the energies of states which, in the absence of the trap, correspond to three free atoms approach values independent of $a$ and $θ$. For other states the $θ$ dependence of the energy is strong, but the energy is independent of $a$ for $|a/a_{\mathrm osc}|\gg1$.