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--Schrödinger 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.

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