A new formulation of the theory of strong coupling

Abstract

Using the scalar symmetrical theory with a fixed and extended source as a model, we show how, in a simple way, the Hamiltonian can be written as H = Ho + gV, where V is independent of the coupling constant g. The term Ho, which does depend on g, can easily be diagonalized. We demonstrate that the effect of gV on the energy spectrum is small for large as well as for small g. The Schrödinger equation takes a form which allows not only the determination of extra terms in the asymptotic expansion of the energy, but also a fast and accurate numerical calculation for all values of the coupling constant. This makes it possible to compare and evaluate the one- and two-point Padé and other approximations.