Exact bound state solutions of the radial Schrödinger equation for the Coulomb potential by conformable Nikiforov–Uvarov approach

Abstract In this work, we investigate the use of the conformable Nikiforov–Uvarov (CNU) method to solve the radial Schrödinger equation exactly for the Coulomb potential. Analytical solutions to the radial Schrödinger equation, which describe how a quantum particle behaves under Coulomb potentials, are frequently challenging. The CNU approach allows us to convert the radial Schrödinger problem into a form that can be solved exactly by the Nikiforov–Uvarov technique, which is well known for its capacity to solve a large class of second-order linear differential equations. We apply the method to the Coulomb potential and obtain accurate formulations for the energy eigenvalues and associated wavefunctions by applying suitable boundary conditions. This method offers a strong framework for examining more intricate quantum systems and provides precise solutions for common potential models. The outcomes offer important new information on quantum mechanical systems with central potentials and demonstrate the effectiveness of the CNU approach in solving the radial Schrödinger equation, particularly when considering fractional dynamics.