In 1963, a simplified approach was developed to study the ground-state energy of an interacting Bose gas with a purely repulsive potential. It consists in the derivation of an equation, which is not based on perturbation theory and which gives the exact expansion of the energy at low densities. This equation is expressed directly in the thermodynamic limit and only involves functions of three variables, rather than $3N$. Here, we revisit this approach, introduce two more equations, and show that these yields accurate predictions for various observables for all densities for repulsive potentials with positive Fourier transform. Specifically, in addition to the ground-state energy, we have shown that the simplified approach gives predictions for the condensate fraction, two-point correlation function, and momentum distribution. We have carried out a variety of tests by comparing the predictions of the equations with quantum Monte Carlo calculations for exponential interaction potentials as well as a different, finite range potential of positive type, and have found remarkable agreement. We thus show that the simplified approach provides an alternative theoretical tool to understand the behavior of the many-body Bose gas, not only in the small and large density ranges, which have been studied before, but also in the range of intermediate density, for which much less is known.

中文翻译：

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从低密度到高密度排斥性Bose气体的简化方法及其数值精度

1963年，开发了一种简化方法来研究具有纯排斥势的相互作用的Bose气体的基态能量。它包含一个方程式的推导，该方程式不是基于微扰理论，而是给出了低密度时能量的精确扩展。该方程式直接以热力学极限表示，仅涉及三个变量的函数，而不是$3ñ$。在这里，我们重新研究这种方法，引入了两个方程，并表明这些方程可对所有观测值产生准确的预测。正傅里叶变换的排斥势的密度。具体来说，除了基态能量外，我们还表明，简化方法可以预测凝结水分数，两点相关函数和动量分布。通过将方程式的预测与量子蒙特卡洛计算的指数相互作用势以及正类型的不同有限范围势进行比较，我们进行了各种测试，并且发现了显着的一致性。因此，我们表明，简化方法为了解多体玻色气体的行为提供了一种替代性的理论工具，不仅在以前研究过的小密度和大密度范围内，而且在中等密度范围内，对于鲜为人知的。