  Using a particular Hilbert space representation of minimum-length deformed
quantum mechanics, we show that the resolution of the wave-function
singularities for strongly attractive potentials, as well as cosmological
singularity in the framework of a minisuperspace approximation, is uniquely
tied to the fact that this sort of quantum mechanics implies the reduced
Hilbert space of state-vectors consisting of the functions nonlocalizable
beneath the Planck length. (Corrections to the Hamiltonian do not provide such
an universal mechanism for avoiding singularities.) Following this discussion,
as a next step we take a critical view of the meaning of wave-function in such
a quantum theory. For this reason we focus on the construction of current
vector and the subsequent continuity equation. Some issues gained in the
framework of this discussion are then considered in the context of field
theory. Finally, we discuss the classical limit of the minimum-length deformed
quantum mechanics and its dramatic consequences.
