Analytical-Numerical Calculation of Energy Levels and Wave Functions of a Conical Quantum Dot as Functions of Apex Angle

In this paper, a conical quantum dot with apex angle α and spherical base of radius R is considered and itsenergy levels and wave functions are calculated. First, using the simple model of an infinite potential well for quantumdots, the Schrödinger equation in spherical coordinates is separated and the governing equations of azimuthal (m) andpolar (ν) quantum numbers for such a conical dot are analytically obtained. Then, the values of ‘ν’ and, hence, allowedenergy levels for the conical dot are numerically calculated. Calculations show that for a fixed value of ‘m’, the intervalbetween ν values decreases with apex angle. For fixed values of ‘m’ and ‘ν’ the energies of ground state and first excitedstate are also numerically calculated. The results show that in conical quantum dots with fixed volume (but with differentangles and radii) the interval between energy levels increases with apex angle. Finally, the wave functions for somespecial cases are plotted.

Keywords:

Conical quantum dot , Polar quantum number , Energy level , Wave function