We study a system of $N$ Bose atoms trapped by a symmetric harmonic potential, interacting via weak central forces. Considering the ground state of the rotating system as a function of the two conserved quantities, the total angular momentum and its collective component, we develop an algebraic approach to derive exact wave functions and energies of these ground states. We describe a broad class of the interactions for which these results are valid. This universality class is defined by simple integral condition on the potential. Most of the potentials of practical interest which have pronounced repulsive component belong to this universality class.
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机译：我们研究了一个由对称谐波势俘获的$ N $玻色子原子的系统，该系统通过弱中心力相互作用。考虑到旋转系统的基态是两个守恒量，总角动量及其集合分量的函数，我们开发了一种代数方法来导出这些基态的精确波函数和能量。我们描述了对这些结果有效的一类广泛的相互作用。该通用性类别是通过对势的简单积分条件定义的。具有排斥性的大部分具有实践意义的潜力都属于这一普遍性类别。
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