6 research outputs found
Sum rules in the oscillator radiation processes
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.Comment: comments and references added, LaTe
An Exact Approach to the Oscillator Radiation Process in an Arbitrarily Large Cavity
Starting from a solution of the problem of a mechanical oscillator coupled to
a scalar field inside a reflecting sphere of radius , we study the behaviour
of the system in free space as the limit of an arbitrarily large radius in the
confined solution. From a mathematical point of view we show that this way of
facing the problem is not equivalent to consider the system {\it a} {\it
priori} embedded in infinite space. In particular, the matrix elements of the
transformation turning the system to principal axis, do not tend to
distributions in the limit of an arbitrarily large sphere as it should be the
case if the two procedures were mathematically equivalent. Also, we introduce
"dressed" coordinates which allow an exact description of the oscillator
radiation process for any value of the coupling, strong or weak. In the case of
weak coupling, we recover from our exact expressions the well known decay
formulas from perturbation theory.Comment: 27 page