Spatial Regularization of Green’s Function in an Electric Field and the Quasi-Classical Complex Energy Spectrum in Quantum Dots

It is shown that the spatial regularization of Green’s function (in fact, the introduction of a finite source radius) in an electric field makes it possible to solve the problem of calculating the spectrum of weakly bound states in quantum dots in a new way. The physical meaning of the stationary phase points in Green’s function is clarified, so that the calculation of the Stark shift and the ionization probability becomes completely semiclassical. A new quantization rule is obtained for the parameters of quantum dots, under which there are weakly bound states in them, well controlled by external fields.