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

• URL: http://arxiv.org/abs/2402.01409v1
• Date: Fri, 2 Feb 2024 13:42:39 GMT
• Title: Analytical solutions of the Schr\"{o}dinger equation for two confined atoms with van der Waals interaction
• Authors: Ruijie Du
• Abstract summary: We derive solutions of the Schr"odinger equation for the isotropic van der Waals interaction in a symmetric harmonic trap. We deduce the energy spectrum of the two-body relative motion and relate the spectrum to scattering lengths for $s$ wave and $p$ wave.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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