  We consider the problem of an harmonic oscillator coupled to a scalar field
in the framework of recently introduced dressed coordinates. We compute all the
probabilities associated with the decay process of an excited level of the
oscillator. Instead of doing direct quantum mechanical calculations we
establish some sum rules from which we infer the probabilities associated to
the different decay processes of the oscillator. Thus, the sum rules allows to
show that the transition probabilities between excited levels follow a binomial
distribution.
