OICC Press Journal of Theoretical and Applied Physics 2251-7235 17 4 2023 05 30 Quantum mechanical treatment of Shannon entropy measure and energy spectra of selected diatomic molecules with the modified Kratzer plus generalized inverse quadratic Yukawa potential model 10.57647/J.JTAP.2023.1704.40 EN Etido P. Inyang Department of Physics, National Open University of Nigeria, Jabi, Abuja, Nigeria 0000-0002-5031-3297 Ituen B. Okon Department of Physics, University of Uyo, Uyo, Nigeria Fina O. Faithpraise Department of Physics, University of Calabar, Calabar, Nigeria. Eddy S. William Theoretical Physics Group, Department of Physics, School of Pure and Applied Sciences, Federal University of Technology, Ikot Abasi, Nigeria. Peter O. Okoi Department of Physics, University of Calabar, Calabar, Nigeria. Efiong A. Ibanga Department of Physics, National Open University of Nigeria, Jabi, Abuja, Nigeria Journal Article 2023 05 30 In this research, we have obtained the energy eigenvalues and the corresponding normalized eigenfunction for the linear combination of the modified Kratzer and generalized inverse quadratic Yukawa potential using two different analytical methods: the exact quantization rule and the formula method respectively. The obtained normalized wave function is used to study the Shannon entropy in position and momentum spaces for the ground and first excited states. It was observed that the Shannon entropy in position space decreases as the screening parameter is increased and also increases in momentum space as the screening parameter is increased in such a way that their sum satisfies the Bialynicki-Birula-Mycielski (BBM) inequality that stipulated lower bound state of Sr+Sp>D(l+In(pi)) . Numerical results were generated for some selected diatomic molecules such as N2, CO, NO, and CH which agreed with other works in the literature. The content of this research finds application in atomic and molecular physics, quantum chemistry, and physics.