Evolution of quasi-stationary states of an electron in an open spherical quantum dot

Abstract

A theory of the evolution of spectral parameters of quasi-stationary states of an electron in an open spherical quantum dot is proposed in terms of the effective-mass and rectangular potential barrier model. The probability distribution functions (over the quasi-momentum or the energy) of electron location within the open quantum dot and their spectral characteristics, such as generalized resonance energies and generalized resonance widths, are introduced. It is demonstrated that, as the barrier layer thickness varies from zero to infinity, generalized resonance energies and the generalized resonance widths determined by the distribution function method satisfy the Heisenberg uncertainty principle, whereas the resonance energies and resonance widths determined from the poles of the scattering matrix for small thicknesses of the barrier layer do not obey this principle.