Prolate spheroidal quantum dot: Electronic states, direct interband light absorption and electron dipole moment

Excitonic states and direct interband light absorption are considered in prolate spheroidal quantum dot. The problem of finding the one electron wave function and energy spectrum have been solved exactly. Three regimes of size quantization have been considered. Absorption edge dependence on the small semiaxes of the spheroid has been obtained. The probability of the direct interband transitions has been calculated and the selection rules for quantum numbers have been obtained. It has been shown that in prolate spheroidal quantum dot the exact value of the electron ground state with high accuracy coincides with the value of ground state in strongly prolate ellipsoidal quantum dot obtained in the framework of the adiabatic approximation. The dependence of z component of the electron dipole moment has been studied on the small semiaxes of the prolate spheroidal quantum dot.