Analytic structure of the damped driven Morse oscillator

Abstract

An investigation of the analytic structure of the solution of the damped and driven Morse oscillator is carried out after effecting an exponential transformation. From the psi series representation, the local behaviour in the neighbourhood of a movable singularity is mapped onto a simple solvable differential equation admitting hyperbolic function solution. The inverse map reveals the existence of a two-armed infinite sheeted Riemann structure of the singularities for the system.