Angular minimum uncertainty states with large uncertainties
  The uncertainty relation for angle and angular momentum has a lower bound which depends on the form of the state. Surprisingly, this lower bound can be very large. We derive the states which have the lowest possible uncertainty product for a given uncertainty in the angle or in the angular momentum. We show that, if the given angle uncertainty is close to its maximum value, the lowest possible uncertainty product tends to infinity. 
Joerg B. Goette, Paul M. Radmore, Roberta Zambrini and Stephen M.   Barnett