biostudies-literatureUnknown22Liu YWe show that a system consisting of two interacting particles with mass ratio 3 or 1/3 in a hard-wall box can be exactly solved by using Bethe-type ansatz. The ansatz is based on a finite superposition of plane waves associated with a dihedral group D₆, which enforces the momentums after a series of scattering and reflection processes to fulfill the D₆ symmetry. Starting from a two-body elastic collision model in a hard-wall box, we demonstrate how a finite momentum distribution is related to the D_2n symmetry for permitted mass ratios. For a quantum system with mass ratio 3, we obtain exact eigenenergies and eigenstates by solving Bethe-type-ansatz equations for arbitrary interaction strength. A many-body excited state of the system is found to be independent of the interaction strength, i.e., the wave function looks exactly the same for non-interacting two particles or in the hard-core limit.iScience181-194https://www.ebi.ac.uk/biostudies/studies/S-EPMC6911986biostudies-literatureMass-Imbalanced Atoms in a Hard-Wall Trap: An Exactly Solvable Model Associated with D₆ Symmetry.PMC6911986Liu YZhang YQi FChen SfalseMass-Imbalanced Atoms in a Hard-Wall Trap: An Exactly Solvable Model Associated with D₆ Symmetry.We show that a system consisting of two interacting particles with mass ratio 3 or 1/3 in a hard-wall box can be exactly solved by using Bethe-type ansatz. The ansatz is based on a finite superposition of plane waves associated with a dihedral group D₆, which enforces the momentums after a series of scattering and reflection processes to fulfill the D₆ symmetry. Starting from a two-body elastic collision model in a hard-wall box, we demonstrate how a finite momentum distribution is related to the D_2n symmetry for permitted mass ratios. For a quantum system with mass ratio 3, we obtain exact eigenenergies and eigenstates by solving Bethe-type-ansatz equations for arbitrary interaction strength. A many-body excited state of the system is found to be independent of the interaction strength, i.e., the wave function looks exactly the same for non-interacting two particles or in the hard-core limit.2019-01-01T00:00:00Z2019 Dec2022-02-09T12:23:39.049Z2020-05-21T23:35:23ZS-EPMC69119863178555610.1016/j.isci.2019.11.018