  A simple theoretical model of scalar fields in one spatial dimension with
internal symmetry is considered. Assuming the existence of localized classical
field configurations, the Schr\"{o}dinger picture is used to describe their
quantum properties. Using the collective coordinates method for the
Schr\"{o}dinger equation allows the development of a perturbation theory that
accurately describes the symmetry properties of the theory. Examples of $U(1)$
and $SU (2)$ symmetries are analyzed and the discreteness of the energy of
bound states is shown as a result of the symmetry of the theory.
