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Taking into account the importance of the unified theory of quantum mechanicsand gravity, and the existence of a minimum length of the order of the Planckscale, we consider a modified Schr\"odinger equation resulting from ageneralised uncertainty principle, which finds applications from the realm ofquantum information to large-scale physics, with a quantum mechanicallycorrected gravitational interaction proposed very recently. As the resultingequation cannot be solved by common exact approaches, including Heun or Liealgebraic ones, we propose a Bethe-Ansatz approach, which will be applied andwhose results we discuss.

On Some Quantum Correction to the Coulomb Potential in Generalized Uncertainty Principle Approach