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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.01409 |
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Table of Contents:
- We derive solutions of the Schrödinger 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.