Convergent Perturbation Theory for a q-deformed Anharmonic Oscillator
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hep-th
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anharmonicdeformedoscillatorperturbationbecomesboundedcloseconvergence
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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.
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