The Magnetic and Aharonov-Bomh Flux Fields of Carbon Monoxide Diatomic Molecule with Energy-Dependent Screened Kratzer Potential

An energy-dependent potential is a type of quantum mechanical potential in which the potential energy explicitly depends on the particle’s energy, rather than solely on its spatial coordinates as in conventional potentials. Energy-dependent potentials (EDPs) have gained attention in quantum mechanics due to their ability to model systems where the interaction strength varies with the particle’s energy, offering a more flexible description of molecular and nuclear interactions than conventional static potentials. This study analytically solves the two-dimensional Schrödinger equation with an Energy-Dependent Screened Kratzer Potential (EDSKP) using the Nikiforov-Uvarov (NU) method to obtain the energy eigenvalues of a carbon monoxide (CO) diatomic molecule under the influence of Magnetic and Aharonov-Bohm (AB) flux fields. The energy spectra are computed for different quantum numbers, showing that the energy levels decrease with increasing magnetic and AB-flux field strength. This decrease is more pronounced when the energy slope parameter is negative, indicating a field-induced stabilization of the molecule. Conversely, the energy levels increase rapidly when the energy slope parameter is positive, reflecting a stiffening interaction. These behaviors are graphically confirmed and offer insights into the quantum mechanical response of molecules under external perturbations. By adjusting the potential parameters, the well-known screened Kratzer potential model is recovered. In the absence of external fields and with a substitution for the magnetic quantum number, the energy eigenvalue of the three-dimensional Schrödinger equation is retrieved as a special case, which aligns with previous studies. These results provide useful perspectives for molecular physics, quantum control, and materials science