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arXiv · 2402.01409

Analytical solutions of the Schr\"{o}dinger equation for two confined atoms with van der Waals interaction

Ruijie Du
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Abstract

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.

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Ruijie Du. 2024-02-02. Analytical solutions of the Schr\"{o}dinger equation for two confined atoms with van der Waals interaction. https://doi.org/10.1007/s00601-024-01970-w

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