The solution is the wavefunction , shown on the upper left, with the allowed energy levels for (For , the solutions are spherical Bessel functions.)

The electron's probability density curve is given by the square of the wavefunction, determining the probability of finding the electron at a given radius from the center of the nanoparticle, as shown on the upper right.

The lower-left graph shows the probability density in three dimensions.

At the lower right is an energy level diagram for the electrons, showing the relative spacings of the .