Quantum mechanical model of localized electrons on the surface of polymer nanospheres

We examine the quantum mechanics of a simple model for charged dielectric nanospheres called quantum drops. The model, previously introduced in semiclassical quantization work, involves one electron moving in an effective potential field due to N−1 other electrons on the surface of a nanosphere. We discuss how electron confinement occurs and how energy levels exhibit scaling properties similar to those expected for a particle moving in a restricted, two-dimensional area.