The Schrödinger equation has been solved for the Hulthén plus screened Kratzer Potential (HSKP) via the Nikiforov-Uvarov-Functional Analysis (NUFA) method. The bound state energy and wave function for the HSKP have been obtained in closed form by applying the Greene-Aldrich approximation scheme to the inverse square term. Using the resulting energy equation, we computed the energy spectra for twelve diatomic molecules (CuLi, TiH, VH, TiC, HCl, LiH, H₂, ScH, CO, I₂, N₂, and NO) for various quantum states. In order to show the accuracy of our procedure, four special cases of the collective potential were obtained, and the results are in excellent agreement with the existing literature.

In this study, the Schrödinger equation with the Hulthén plus screened Kratzer potentials (HSKP) are solved via the Nikiforov-Uvarov (NU) and the series expansion methods. We obtained the energy equation and the wave function in closed form with Greene-Aldrich approximation via the NU method. The series expansion method was also used to obtain the energy equation of HSKP. Three distinct cases were obtained from the combined potentials. The energy eigenvalues of HSKP for HCl, LiH, H2, and NO diatomic molecules were computed for various quantum states. To test the accuracy of our results, we computed the bound states energy of HCl and LiH, for a special case of Kratzer and screened Kratzer potentials, which are in excellent agreement with the report of other researchers.

The solutions of the Schrödinger equation are obtained with an inversely quadratic Yukawa potential using the Nikiforov-Uvarov-Functional-analysis method. The energy spectrum and wave function were obtained in closed form. The energy equation was used to predict the masses of the heavy mesons such as charmonium (сĉ) and bottomonium (bḃ) for different quantum numbers. The results obtained agreed with other theoretical predictions and experimental data with a percentage error of 1.68 % and 0.50 % for charmonium (сĉ) and bottomonium (bḃ) respectively.

In this research, we model Hulthén plus generalized inverse quadratic Yukawa potential to interact in a quark-antiquark system. The solutions of the Schrödinger equation are obtained using the Nikiforov-Uvarov method. The energy spectrum and normalized wave function were obtained. The masses of the heavy mesons for different quantum states such as 1S, 2S , 1P, 2P 3S, 4S, 1D, and 2D were predicted as 3.096 GeV, 3.686 GeV, 3.327 GeV, 3.774GeV, 4.040 GeV, 4.364GeV, 3.761 GeV, and 4.058 GeV respectively for charmonium (cc). Also, for bottomonium (bb) we obtained 9.460 GeV, 10.023 GeV, 9.841 GeV, 10.160 GeV, 10.345 GeV, 10.522 GeV, and 10.142GeV for different states of 1S , 2S , 1P , 2P , 3S , 4S , 1D respectively. The partition function was calculated from the energy spectrum, thereafter other thermal properties were obtained. The results obtained showed an improvement when compared with the work of other researchers and excellently agreed with experimental data with a percentage error of 1.60 % and 0.46 % for (cc) and (bb), respectively.

The hybridization of renewable energy resources technology is one of the emerging trends in the area of science and technology. The idea is spreading very wide not only within households but industries because of its numerous benefits such as its ecofriendly nature, cost effectiveness, and accessibility. This paper focuses on reviewing the hybridization of wind and solar energy sources in Nigeria. Wind speeds are considerably low during dry season in Nigeria when the intensity of the sun is very high and shines for a long period of time. The wind is stronger during the rainy season when less sunlight is available. Since the maximum operating time for solar and wind systems occur at different times of the day and year, power generation using wind solar hybrid system is likely to be readily available when needed. Wind and solar hybrid system conversion could be large scale connected to the national grid or small scale for stand-alone systems. Different work carried out by researchers' shows that if Nigeria can properly harness 40 percent of her renewable energy resources such as wind and solar, the problem of power failure will be a thing of the past in both remote locations and urban areas of Nigeria. It is recommended that government should as a matter of urgency prioritize the generation of electricity through the integration of the various renewable energy resources.