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Two interacting fermions in a 1D harmonic trap: matching the Bethe ansatz and variational approaches

In this work, combining the Bethe ansatz approach with the variational principle, we calculate the ground state energy of the relative motion of a system of two fermions with spin up and down interacting via a delta-function potential in a 1D harmonic trap. Our results show good agreement with the analytical solution of the problem, and provide a starting point for the investigation of more complex few-body systems where no exact theoretical solution is available.

preprint2012arXivOpen access
D. RubeniA. FoersterI. Roditi
cond-mat.quant-gas
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Open access3 authors1 topic
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D. RubeniA. FoersterI. Roditi

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