Resonance energy and width operators in dilatation transformed dynamical systems

This Letter is concerned with locating dynamical resonances, as well as with algebraic calculations of resonance energy and lifetime based on rigged Hilbert space analysis. We present a derivation, from complex dilatation transformation, of a pair of operators corresponding to dynamical resonance energy and resonance width. These operators yield the well-known results for the case of a harmonic system. We also illustrate the resonance and lifetime calculation by application to dynamical resonances supported by a Morse potential barrier.