Electron and Exciton Quasi-Stationary s-States in Open Spherical Quantum Dots

The theoretical calculation of spectral parameters of electron and exciton quasi-stationary s-states in open spherical quantum dot is performed within the effective mass approximation and rectangular potentials model. The conceptions of probability distribution functions (over quasi-momentum or energy) of electron location inside of quantum dot and their spectral characteristics: generalized resonance energies and widths are introduced. It is shown that the generalized resonance energies and widths, obtained within the distribution functions, satisfy the Heisenberg uncertainty principle for the barrier widths varying from zero to infinity. At the same time, the ordinary resonance energies and widths defined as complex poles of scattering S-matrix, do not satisfy it for the small barrier widths and, therefore, are correct only for the open quantum dots with rather wide potential barriers.