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arXiv · 1706.04413

The Goldilocks model of separable, zero-range, few-body interactions in one-dimensional harmonic traps

Molte Emil Strange Andersen·N. L. Harshman·Nikolaj Thomas Zinner
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Abstract

This article introduces the "Goldilocks model" for a few repulsively interacting particles trapped in a one-dimensional harmonic well and provides exact solutions for the three-particle case. The Goldilocks model shares features with two other well-known systems, the Calogero model and the contact-interaction model, and coincides with them in limiting cases. However, those models have purely two-body interactions whereas this model has intrinsically few-body interactions. Comparing these three models provides clarifying distinctions among the properties of symmetry, separability and integrability. The model's analytic solutions provide a useful basis to improve approximation schemes, especially near the unitary limit of hard-core contact interactions.

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Molte Emil Strange Andersen, N. L. Harshman, Nikolaj Thomas Zinner. 2017-08-16. The Goldilocks model of separable, zero-range, few-body interactions in one-dimensional harmonic traps. https://doi.org/10.1103/physreva.96.033616

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