Quantum Model of a Trapezoidal Limiting Potential Profile in a Spherical Nanocrystal

Abstract

The limiting potential model is considered for a spherical quantum dot with three variation parameters–the well depth, external and internal radii. The stationary s-states are computed by way of the exact solution and in the WKB approximation. If the quasiclassical conditions are met, the approximate consideration is applied for the states with l ≠ 0. As a result, the energy values of the lower bound states are presented at the fixed external and varying internal radii in the wells of various depths. The dependence of the energy gap between the levels in the well on the variation parameters is shown.