Two-electron states and state exchange time control in parabolic quantum dot

•Two-electron states in a spherically symmetric parabolic QD were considered.•Using uncertainty relations the ground-state energy estimation was made.•The dependence of ground-state energy on the QD size was studied.•The state exchange time dependence on the QD size were obtained.

Using the Heisenberg uncertainty relationship and the stationary perturbation theory we consider two-electron states in a spherically symmetric parabolic quantum dot (parabolic helium atom). The dependence of ground-state energy on the QD size is studied. The energy of two-electron system monotonically decreases with QD radius increase. The problem of the state exchange time control in QD is discussed, taking into account the spins of the electrons in the Russell–Saunders approximation. With the increase of the QD radius the state exchange time increases.