The envelope theory is a simple technique to obtain approximate, but reliable, solutions of many-body systems with identical particles. The accuracy of this method is tested here for two systems in one dimension with pairwise forces. The first one is the fermionic ground state of the analytical Calogero model with linear forces supplemented by inverse-cube forces. The second one is the ground state of up to 100 bosons interacting via a Gaussian potential. Good bounds can be obtained depending on values of the model parameters.

中文翻译：

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一维包络理论的检验

包络理论是一种简单的技术，用于获得具有相同粒子的多体系统的近似但可靠的解。此处针对具有成对力的一维中的两个系统测试了该方法的准确性。第一个是解析 Calogero 模型的费米子基态，线性力由反立方力补充。第二个是多达 100 个玻色子通过高斯势相互作用的基态。可以根据模型参数的值获得良好的界限。