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The envelope theory is a simple technique to obtain approximate, but reliable, solutions of manybody 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. *

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No abstract

The envelope theory is an easy-to-use approximation method to obtain eigensolutions for some quantum many-body systems. Even if the solutions are reliable and an improvement procedure exists, the method can lack of accuracy for some systems. In a previous work, two hypotheses were proposed to explain the low precision: the presence of a divergence in the potential and a mix of variational characters. In the present work, different systems are studied to test these hypotheses. Theses tests show that the presence of a divergence causes indeed less accurate results, while the mix of variational characters reduces the impact of the improvement procedure.