  One of the most widely problem studied in quantum mechanics is of an infinite
square-well potential. In a minimal-length scenario its study requires
additional care because the boundary conditions at the walls of the well are
not well fixed. In order to avoid this we solve the finite square-well
potential whose the boundary conditions are well fixed, even in a
minimal-length scenario, and then we take the limit of the potential going to
infinity to find the eigenfunctions and the energy equation for the infinite
square-well potential. Although the first correction for the energy eigenvalues
is the same one has been found in the literature, our result shows that the
eigenfunctions have the first derivative continuous at the square-well walls
what is in disagreement those previous work. That is because in the literature
the authors have neglected the hyperbolic solutions and have assumed the
discontinuity of the first derivative of the eigenfunctions at the walls of the
infinite square-well which is not correct. As we show, the continuity of the
first derivative of the eigenfunctions at the square-well walls guarantees the
continuity of the probability current density and the unitarity of the time
evolution
