Quasistationary states of an electron in open quantum dots

The quasistationary states of an electron in a spherically N-layered open quantum dot are investigated. A novel complex eigen-solver is presented to determine both the resonance positions E_R and the corresponding lifetimes τ of the system. In this eigen-solver, the wave functions are expressed in terms of the Whittaker functions with complex arguments, and the effective-mass Schrodinger equation is solved analytically. The quasistationary states in terms of the complex eigen-energies, E_R-ih/(2τ), are extracted numerically in the complex plane by Newton´s method. All the quasistationary states of the system can be determined via this eigen-solver. For illustration, the numerical calculations are carried out for the HgS/CdS/HgS multi-layered quantum dot. Both the energy levels and the lifetimes of the quasistationary states are found as functions of the geometric parameters of the system. The lifetime of an electron in such a system is very sensitive to the geometric characteristics.