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Updated: Feb 16, 2026

Associated Chromosome Trap for Identifying Long-range DNA Interactions
Published on: April 23, 2011
Exactly solvable model of two trapped quantum particles interacting via finite-range soft-core interactions
Przemysław Kościk1, Tomasz Sowiński2
1Institute of Physics, Jan Kochanowski University, ul. Świętokrzyska 15, PL-25406, Kielce, Poland.
Abstract:
The exactly solvable model of two indistinguishable quantum particles (bosons or fermions) confined in a one-dimensional harmonic trap and interacting via finite-range soft-core interaction is presented and many properties of the system are examined. Particularly, it is shown that independently on the potential range, in the strong interaction limit bosonic and fermionic solutions become degenerate. For sufficiently large ranges a specific crystallization appears in the system. The results are compared to predictions of the celebrated Busch et al. model and those obtained in the Tonks-Girardeau limit. The assumed inter-particle potential is very similar to the potential between ultra-cold dressed Rydberg atoms. Therefore, the model can be examined experimentally.
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