  Taking into account the importance of the unified theory of quantum mechanics
and gravity, and the existence of a minimal length of the order of the Planck
scale, we consider a modified Schr\"odinger equation resulting from a
generalized uncertainty principle, which finds applications from the realm of
quantum information to large-scale physics, with a quantum mechanically
corrected gravitational interaction proposed very recently. As the resulting
equation cannot be solved by common exact approaches, we propose a Bethe ansatz
approach, which will be applied and whose results we will discuss, commenting
on the analogy of the present study with some other interesting physical
problems.
