Energy spectra of Hartmann and ring-shaped oscillator potentials using the quantum Hamilton–Jacobi formalism

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In the present work, we apply the exact quantization condition, introduced within the framework of Padgett and Leacock's quantum Hamilton–Jacobi formalism, to angular and radial quantum action variables in the context of the Hartmann and the ring-shaped oscillator potentials which are separable and non-central. The energy spectra of the two systems are exactly obtained.