Though the Rayleigh-Schrödinger perturbation theory (PT) is a very old issue, the necessary and sufficient conditions of the convergence of this series are still not known. This is not only of theoretical interest, since the perturbational expansion of the correlation energy in many-body perturbation theory is often divergent in practice.
In this seminar, we investigate two issues:
1) Is it possible to convert a divergent PT to a convergent one by redefining the partitioning, that is by redefining the zero order Hamiltonian?
2) Knowing the members of the divergent series, is it possible to set up a mathematical tool to estimate the exact physical result from the partial sums?
As to question 2), a classical affirmative answer is to use Pade approximants for resummation. However, we have found that they are not very useful in practice. Instead, we investigate the possibility to scale down the divergent contributions, making them convergent thereby, and try to find analytical continuation of these convergent results to the physical situation with no scaling.