On the symmetry of the electronic density in the three-electron parabolic quantum dot

The structure of the lowest states of a three-electron axially symmetric parabolic quantum dot in a zero magnetic field is investigated. It is shown that the electronic density of the triplet states possesses certain approximate symmetry which is best seen when using Dalitz plots as the visualization tool. It is demonstrated that the origin of that symmetry is caused by the symmetry of the potential energy in the vicinity of its minimum. The discovered symmetry could provide an insight into the problem of the separation of slow and fast variables in the Schro\"dinger equation for the axially or spherically symmetric quantum dots.