Coherent states for continuous spectrum operators with non-normalizable   fiducial states
  The problem of building coherent states from non-normalizable fiducial states is considered. We propose a way of constructing such coherent states by regularizing the divergence of the fiducial state norm. Then, we successfully apply the formalism to particular cases involving systems with a continuous spectrum: coherent states for the free particle and for the inverted oscillator $(p^2 - x^2)$ are explicitly provided. Similar ideas can be used for other systems having non-normalizable fiducial states. 
Joseph Ben Geloun, Jeff Hnybida and John R. Klauder
math-ph math.MP quant-ph