A sufficient condition for the angle parameter of the complex dilatation transformation

Abstract

We discuss a sufficient condition for the determination of the angle parameter of the complex dilatation transformation that is often used for the location of dynamical resonances. We show, as one example, that the proposed condition yields the exact value of this angle parameter for the case of a harmonic potential. The formulation of the sufficient condition permits it to be used for general potentials. We illustrate the utility of the proposed method by calculating the location of the resonance supported by a potential introduced in a model study by Moiseyev, Certain and Weinhold. The results obtained are very close to, but more accurate than, those previously reported, and they are obtained with less computational effort.