Expectation values and energy spectra of selected diatomic molecules: a Nikiforov-Uvarov approach - Inyang, Etido P (Journal of Physics: Theories and Applications, 2000)
This study employs the Nikiforov-Uvarov method to solve the Schrödinger equation for the class of inversely quadratic Yukawa potential (CIQYP), deriving both the energy eigenvalues and the corresponding wave functions. The eigenvalues of the CIQYP for three diatomic molecules (N₂, O₂, and NO) are determined using their specific molecular data. The results reveal that the bound-state energy spectra of these molecules increase with both the principal and angular momentum quantum numbers. Numerical calculations of expectation values were performed, and the potential model simplifies to the Kratzer potential under specific boundary conditions, ensuring analytical consistency. Additionally, the energy spectra of other diatomic molecules, such as I₂ and CO, are analyzed. For a fixed principal quantum number, the energy spectrum increases with rising angular momentum quantum numbers, aligning closely with results from other established analytical methods. The analysis of diatomic molecules under the CIQYP provides valuable insights into their energy states, with significant implications for molecular physics, materials science, and astrophysics.