TY - JOUR
AU - Escobar-Ruiz, Adrian M.
AU - Montoya, Fidel
PY - 2022/02/28
Y2 - 2024/04/15
TI - Generalized three-body harmonic oscillator system: ground state
JF - Acta Polytechnica
JA - Acta Polytech
VL - 62
IS - 1
SE - Analytic and Algebraic Methods in Physics
DO - 10.14311/AP.2022.62.0050
UR - https://ojs.cvut.cz/ojs/index.php/ap/article/view/7668
SP - 50-55
AB - <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>
ER -