Pseudoharmonic oscillator in quantum mechanics with a minimal length

The pseudoharmonic oscillator potential is studied in non-relativistic quantum mechanics with a generalized uncertainty principle characterized by the existence of a minimal length scale, [Formula: see text]. By using a perturbative approach, we derive an analytical expression of the energy spectrum in the first-order of the minimal length parameter β. We investigate the effect of this fundamental length on the vibration–rotation energy levels of diatomic molecules through this potential function interaction. We explicitly show that the minimal length would have some physical importance in studying the spectra of diatomic molecules.