Енергетичний спектр електрона в розділених та злитих сферичних квантових точках

Abstract

We present a highly efficient semi-analytical approach to model electronic states in fused spherical quantum dots by deriving an exact analytical Fourier transform of their 3D shape function using cylindrical Bessel functions. This mathematical novelty allows the direct application of the plane-wave expansion method to solve the Schrödinger equation with a spatially dependent effective mass, completely eliminating the need for resource-intensive 3D spatial meshing. Applying this to a GaAs/AlGaAs heterostructure, we demonstrate that strong geometric overlap induces robust quantum-mechanical hybridization, causing an exponential splitting of degenerate energy levels into symmetric and antisymmetric states. The model guarantees an exact asymptotic transition to isolated quantum dot solutions, providing a fast and rigorous tool for prototyping complex nanostructures.