Energy spectrum of ideal quantum dots controlled by an external electric field

We have constructed a theoretical model describing the energy spectrum and autoionisation probability for an ideal quantum dot in the external DC and AC electric fields, free of using the delta-potential approximation and perturbation theory. The wave functions of the electron quasi-stationary states under these conditions are calculated. To this end, we have elaborated a new method for regularising the Gamov wave function used to calculate the complex electron energy, describing both the energy spectrum of the system and the probability of the state decay (autoionisation). The oscillations of the Stark shift and the energy level width due to the DC electric field are found. It is shown that these oscillations essentially affect the energy spectrum of the quantum dot and principally cannot be described within the frameworks of perturbative approaches.