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 \(v\rightarrow v+1, v=0, 1 \ldots 7\) $v\to v+1,v=0,1\dots 7$ in \(J=0,1\ldots 47\) $J=0,1\dots 47$ rotational states of dinitrogen \(^{14}\) ${}^{14}$ N \(_2\) ${}_2$ and \(^{15}\) ${}^{15}$ N \(_2\) ${}_2$ in the ground electronic state \(X^1\Sigma _g^+\) $X^1{\mathrm{\Sigma }}_g^{+}$ . 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 \(^{74}\) ${}^{74}$ Ge \(^{32}\) ${}^{32}$ S, \(^{79}\) ${}^{79}$ Br \(^{35}\) ${}^{35}$ Cl and \(^{1}\) ${}^1$ H \(^{35}\) ${}^{35}$ 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.