Convergent Perturbation Theory for a q-deformed Anharmonic Oscillator
  A $q$--deformed anharmonic oscillator is defined within the framework of $q$--deformed quantum mechanics. It is shown that the Rayleigh--Schr\"odinger perturbation series for the bounded spectrum converges to exact eigenstates and eigenvalues, for $q$ close to 1. The radius of convergence becomes zero in the undeformed limit. 
Rainer Dick, Andrea Pollok-Narayanan, Harold Steinacker, Julius Wess