  We derive solutions of the Schr\"{o}dinger equation for the isotropic van der
Waals interaction in a symmetric harmonic trap, with the recent approach
[arXiv:2207.09377 (2022)] to handle the multi-scale long-range potential.
Asymptotic behaviors of these solutions are then obtained for $r\rightarrow 0$
and $r\rightarrow \infty$. We further deduce the energy spectrum of the
two-body relative motion and relate the spectrum to scattering lengths for $s$
wave and $p$ wave. These results can be used to research trapped atom-atom
collisions and energy spectra.
