Energy and Shannon entropy for a hydrogen atom confined in a dielectric
spherical microcavity
Abstract
We calculate the energy and Shannon entropy for a hydrogen atom confined
in a dielectric spherical microcavity for the fist time. In contrast to
the hydrogen atom in the vacuum microcavity, some unexpected and
interesting phenomena appear: First, the turning radius for the bound
energy changes from positive to negative depends on the dielectric
constant of the spherical microcavity sensitively. With the increase of
the relative dielectric constant, the turning radius gets larger.
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 for the confined hydrogen atom greatly. The
Shannon entropy in the vacuum microcavity is the smallest and the
Shannon entropy increases with the relative dielectric constant. For
smaller size spherical microcavity, the Shannon entropy change is always
negative, which suggests that the electron density is localized. With
the increase of 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 confining
effect of the spherical microcavity on the atom by changing the
dielectric. 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.