Eigenfunctions, uncertainties and thermal properties of diatomic molecules under screened modified Kratzer potential

A new potential model is proposed in this paper. This new potential named the screened modified Kratzer potential is solved within the nonrelativistic regime using Nikiforov–Uvarov-Functional Analysis (NUFA) to obtain the energy spectrum and the corresponding eigenfunction. The numerical results for selected diatomic molecules using the obtained energy spectrum have been obtained, and this is in good agreement with what was obtained using other analytical methods. The vibrational partition function for CO , NO and N 2 diatomic molecules was evaluated via the Euler–Maclaurin approach and other thermal properties such as free energy, entropy, mean energy and specific heat capacity. The expectation values of r , r 2 , p → and p → 2 is also evaluated numerically for different diatomic molecules using the normalized wave function for the two low lying states n = 0 , 1 corresponding to the ground and first excited states. The numerical results for the selected diatomic molecules validates the Heisenberg uncertainty relation, Δ r Δ p ≥ ħ 2 .