Electronic structure of one electron confined in three-dimensional quantum dots

We study the electronic structure of three-dimensional quantum dots with one electron using the canonical formalism. The confining potential is assumed to be spatially isotropic and harmonic. For one electron the energy spectrum, heat capacity and Helmholtz free energy are calculated as a function of temperature and confinement strength. We find that the internal energy for one-electron artificial atoms and the heat capacity are nearly independent of confinement frequency at high temperatures, while at low temperatures the energy-level structure and heat capacity are shown to be strongly dependent on the confinement strength. In addition, the heat capacity decreases less rapidly with increasing confinement frequency at appropriate temperatures and energy levels are almost linear. Also, the Helmholtz-free energy is obtained to test the confinement and stability of the system.