Energy levels of a spherical quantum dot in a confining potential

Using an exact analytical method, we obtain the ground state and the excited states wave functions as well as the corresponding eigenvalues of a spherical quantum dot in the presence of a confining potential which is a combination of linear, Coulomb and quadratic terms. Next, we investigate the quantum dot energy as the potential coefficients are changed. Our study reveals that considering such a confining potential leads to results which are in good agreement with experimental results.