Two electronic states and state exchange time control in spherical nanolayer

► Two electronic states in spherical quantum nanolayer are discussed. ► The analogue of helium atom theory is represented. ► The eigenfunctions and energy states are obtained. ► The dependence of Coulomb correction, exchange energy and unperturbed system energy upon each radius is represented. ► Exchange time of two electron states can be controlled via changing the geometrical parameters of the nanolayer.