@article{Escobar-Ruiz_Montoya_2022, title={Generalized three-body harmonic oscillator system: ground state}, volume={62}, url={https://ojs.cvut.cz/ojs/index.php/ap/article/view/7668}, DOI={10.14311/AP.2022.62.0050}, abstractNote={<p>In this work we report on a 3-body system in a <em>d</em>−dimensional space ℝ<em><sup>d</sup></em> with a quadratic harmonic potential in the relative <em>distances</em> <em>rij</em> = |ri −rj| between particles. Our study considers unequal masses, different spring constants and it is defined in the three-dimensional (sub)space of solutions characterized (globally) by zero total angular momentum. This system is exactly-solvable with hidden algebra <em>sℓ</em><sub>4</sub>(ℝ). It is shown that in some particular cases the system becomes maximally (minimally) superintegrable. We pay special attention to a physically relevant generalization of the model where eventually the integrability is lost. In particular, the ground state and the first excited state are determined within a perturbative framework.</p>}, number={1}, journal={Acta Polytechnica}, author={Escobar-Ruiz, Adrian M. and Montoya, Fidel}, year={2022}, month={Feb.}, pages={50–55} }