Journal
ISCIENCE
Volume 22, Issue -, Pages 181-+Publisher
CELL PRESS
DOI: 10.1016/j.isci.2019.11.018
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Funding
- NSFC [11674201]
- National Key Research and Development Program of China [2016YFA0300600, 2016YFA0302104]
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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 D-6, which enforces the momentums after a series of scattering and reflection processes to fulfill the D-6 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 quantumsystemwith 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.
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