  We studied the hydrogen atom as a system of two quantum particles in
different confinement conditions; a spherical-impenetrable-wall cavity and a
fullerene molecule cage. The motion is referred to the center of spherical
cavities, and the Schr\"{o}dinger equation solved by means of a Generalized
Sturmian Function expansion in spherical coordinates. The solutions present
different properties from the ones described by the many models in the
literature, where the proton is fixed in space and only the electron is
considered as a quantum particle. Our results show that the position of the
proton (i.e. the center of mas of the H atom) is very sensitive to the
confinement condition, and could vary substantially from one state to another,
from being sharply centered to being localized outside the fullerene molecule.
Interchange of the localization characteristics between the states when varying
the strength of the fullerene cage and mass occurred through crossing
phenomena.
