Schrödinger equation was proposed in theoretical physics to provide information and the behavior of a system of particles. The Schrödinger equation was recently solved for a combination of different potentials using different traditional methodologies. The studies do not consider the effect of a barrier between the potentials. In reality, the barrier between the potentials has an effect on the energy eigenvalues. In the present work, a Kratzer-Mie-type potential, a combination of Kratzer and Mie-type-constant potentials, was proposed as the interacting potential. The solutions of the radial Schrödinger equation was obtained in the presence of the combined potentials by considering a barrier between the potentials. The energy equation and the corresponding wave functions were explicitly calculated. The calculations were performed by using the methodology of supersymmetric quantum mechanics. This method involves the proposition of superpotential function as a solution to its Riccati differential equation. Numerical results were generated for some diatomic molecules using the energy equation and the diatomic model parameters. Some expectation values for the combined potential were calculated using Hellmann Feynman Theorem, and the effect of the barrier on the expectation values were numerically studied. It was observed that when a particle moves from the lower end to a higher end of a barrier, it absorbs energy from the system for some time. This same behavior was also noted when the particle penetrates through a barrier. Thus, its vibration will only depend on the initial energy, which is absorbed. It was equally seen that as the width of the barrier becomes larger than the height, the energy of the system decreases drastically.
Exact solution of the Schrödinger equation for a hydrogen atom at the interface between the vacuum and a topologically insulating surface