Dynamical systems defined by geodesic motion on surfaces of constant negative curvature have been a well studied subject in mathematics.[1] Such systems are of interest to physicists because of their classically strongly chaotic behavior and their extension to quantum chaos[1-3] with applications in cosmology[2] and condensed matter.[4] Different types of configuration spaces have been studied in the context of quantum chaos,[1,2] and these include the punctured surfaces (with one or more cusps) which are of interest to us here.