  A projection method is proposed to treat the one-dimensional Schrodinger
equation for a single particle when the Generalized Uncertainty Principle (GUP)
generates an ultraviolet (UV) wavevector cutoff. The existence of a unique
coordinate representation called the naive one is derived from the
one-parameter family of discrete coordinate representations. In this
bandlimited Quantum Mechanics a continuous potential is reconstructed from
discrete sampled values observed by means of a particle in maximally localized
states. It is shown that bandlimitation modifies the speed of the center and
the spreading time of a Gaussian wavepacket moving in free space. Indication is
found that GUP accompanied by bandlimitation may cause departures of the
low-lying energy levels of a particle in a box from those in ordinary Quantum
Mechanics much less suppressed than commonly thought when GUP without
bandlimitation is in work.
