Feature of energy spectra of three-identical-particle systems in two-dimensional space

The Hamiltonian of a model system has been diagonalized numerically to obtain the eigenstates and eigenenergies. Three types of permutation symmetries: the antisymmetric, the mixed symmetric and the symmetric symmetries have been covered. The dynamical parameters (i.e., the particle mass and the particle-particle interaction) are taken appropriately for cu particles, however a series of qualitative features are revealed to be identical with those of quantum dot electronic systems in semiconductor heterojunctions. We stress the importance of quantum mechanical symmetries in the understanding of quantum mechanical few-body systems.