Stark effect dependence on hydrogenic impurity position in a cubic quantum box

We carry out a detailed variational calculation of the binding energies of hydrogenic impurities in a cubic quantum box as a function of both the impurity position and an applied electric field. It is found that the binding energy of the impurities is highly dependent on the impurity position, and the electric field splits the energy of impurities on points of the box which are equivalent in the absence of the electric field. When the impurity is located at the upper half of the cube and the field pushes the particle downwards, then the binding energy decreases, whereas the Stark shift exhibits a minimum.