Quantum mechanical effects for a hydrogen atom confined in a dielectric spherical microcavity

The quantum mechanical effects for a hydrogen atom confined in a dielectric spherical microcavity is discussed for the fist time. Especially we calculate the energy and Shannon entropy of this system. Some unexpected and interesting phenomena appear due to the effect of the dielectric spherical microcavity. Firstly, the energy of this system is not always negative. For smaller spherical microcavity, the energy can be positive. The turning radius for the bound energy changes from positive to negative depends on the dielectric constant of the spherical microcavity sensitively. Second, the dielectric spherical microcavity impacts the rearrangement of the excited state energy, and breaks the energy degeneracy of the excited states. At some given radius, there is energy crossover between different orbital. Third, the dielectric in the spherical microcavity affects the Shannon entropy change for the confined hydrogen atom greatly. When the size of the spherical microcavity is small, the Shannon entropy change is negative, which suggests that the electron density is localized. As we increase the radius of the microcavity, the Shannon entropy change becomes positive, and the confinement of the electron density gets delocalized. Our results show that we can control the quantum mechanical effects of the atom by changing the dielectric constant in the spherical microcavity. This work can guide the future experimental studies for trapping and manipulating of atoms and molecules in the external environment and has some practical applications in metrology and quantum information processing.