Crossing Points in Spectra and Light Absorption in Spheroidal and Cone-Shaped Quantum Dots

We briefly review the analysis of the energy spectrum, the envelope eigenfunctions of electron, hole and exciton states, and the direct interband light absorption in cone-shaped and spheroidal impenetrable quantum dots. We apply high-order finite element method and calculation schemes of Kantorovich method in comparison with the adiabatic approximation (in the strong size quantization limit) for solving boundary-value problems that describe axially symmetric quantum dots. We demonstrate the efficiency of the algorithms and software by benchmark calculations of spectral and optical characteristics of the cone-shaped and spheroidal quantum dots and crossing points in their spectra.