  The relativistic quantum dynamics of an electrically charged particle subject
to the Klein-Gordon oscillator and the Coulomb potential is investigated. By
searching for relativistic bound states, a particular quantum effect can be
observed: a dependence of the angular frequency of the Klein-Gordon oscillator
on the quantum numbers of the system. The meaning of this behaviour of the
angular frequency is that only some specific values of the angular frequency of
the Klein-Gordon oscillator are permitted in order to obtain bound state
solutions. As an example, we obtain both the angular frequency and the energy
level associated with the ground state of the relativistic system. Further, we
analyse the behaviour of an electrically charged particle subject to the
Klein-Gordon oscillator, the Coulomb potential and a linear scalar potential.
