A projection method is proposed to treat the one-dimensional Schrödinger equation for a single particle when the generalized uncertainty principle (GUP) generates an ultraviolet (UV) wave-vector 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 wave packet 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 to be much less suppressed than commonly thought when GUP without bandlimitation is at work.
|Journal||Physical Review D - Particles, Fields, Gravitation and Cosmology|
|Publication status||Published - Apr 22 2013|
ASJC Scopus subject areas
- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)