Equal-factor approach to perturbation theory

A special application of the equal-factor method is used to reformulate perturbation theory. We derive formulas for determining the mth-order equal factors ({f(n)((m))}) and the corresponding mth-order energy corrections {E-n((m))}. A set of the mth-order perturbation energy levels {E-n((m))} thus may be calculated to arbitrarily high order by self-consistent equations. We have applied this so-called equal-factor perturbation to hydrogenlike ions in a potential field - delta/r(2). Our results illustrate important advantages in aspects both of practice and theory. Work is presently underway to introduce the equal-factor assumption to perturbation theory for reformulation of the principle of the first and second kind of balance theory. [S1050-2947(99)01808-9].