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A Classification of mode symmetries
For any form of two-body interaction, the three-particle
Hamiltonian with harmonic trapping given in eq. (12)
is symmetric under the finite group of transformations
given by the particle permutation symmetry of three
identical (but not necessarily indistinguishable) parti-
cles combined with parity inversion about the mini-
mum of the harmonic trapping potential. When these
symmetries are restricted to the relative configuration
space, they realize the point group C
6v
, i.e. the rotation
and reflection symmetries of a hexagon [47–49]. The
Accepted in Quantum 2019-11-15, click title to verify. Published under CC-BY 4.0. 11