Improved rotating Kratzer–Fues oscillator: eigenenergies, eigenfunctions, coherent states and ladder operators

Exact analytical energy formula for the rotating Kratzer–Fues oscillator with (v, J)-dependent potential parameters is obtained. It was used to reproduce the spectral data generated by the vibrational transitions \(v\rightarrow v+1, v=0, 1 \ldots 7\) in \(J=0,1\ldots 47\) rotational states of dinitrogen \(^{14}\)N\(_2\) and \(^{15}\)N\(_2\) in the ground electronic state \(X^1\Sigma _g^+\). Calculations performed for two isotopic variants enabled the selection of the mass-dependent and independent potential parameters defining the model. To check the ability of the eigenenergies derived to reproduce rotational transitions measured with kHz accuracy, calculations for \(^{74}\)Ge\(^{32}\)S, \(^{79}\)Br\(^{35}\)Cl and \(^{1}\)H\(^{35}\)Cl were performed, obtaining agreement between theoretical and experimental results. Minimum uncertainty coherent states and ladder operators for the rotating improved Kratzer–Fues oscillator are also constructed.