Generation of converging Regge-pole bounds: a new formulation of complex rotation quantization

Abstract

We propose an unprecedented bounding theory which generates converging bounds to the Regge poles of rational fraction scattering potentials. This is made possible by the recent work of Handy ( 2001 J. Phys. A: Math. Gen. 34 L271) and Handy and Wang (2001 J. Phys. A: Math. Gen. 34 8297) which transforms the Schrödinger equation into an equivalent fourth-order, lineardifferential equation for the probability density. This new representation is better suited for numerical considerations, since the rapid oscillations of the Regge-pole wavefunction are factored out. More importantly, the moments of the probability density can be constrained (and thereby the underlying complex angular momentum parameter of the effective potential function) through appropriate moment problem theorems, as incorporated within the eigenvalue moment method of Handy and Bessis (1985 Phys. Rev. Lett. 55 931) and Handy et al (1988 Phys. Rev. Lett. 60 253).