to extend the methods related to perturbation theory (PT) on the region where the coupling constant (or perturbation parameter) appears to be strong. I believe that for most problems encountered it may be achieved in two stages: (1) derivation of recurrence relations between PT coefficients which makes it possible to calculate large number of them by computer; (2) selection of suitable generalized summation procedure such as Borel method or Padé approximants in order to transform divergent PT series into convergent sequence of approximants.
In my recent work, the perturbation parameter is 1/N, where N is the dimensionality of space. My plans for the future are related mainly to the second stage.
Prehistory of my present research
In my earliest papers [1, 2] the methods of PT were applied for calculating the energies and widths of bound and exited states in spherically-symmetric screened Coulomb potentials, especially Yukawa potential. We used large-order PT in powers of screening parameter.
Summation of PT series for a well-known problem of Stark effect in a hydrogen atom was considered . . .
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