Some Aspects of Minimal Length Quantum Mechanics

Details Some Aspects of Minimal Length Quantum Mechanics Some Aspects of Minimal Length Quantum Mechanics

2005-07-03

arxiv.org/abs/quant-ph/0507018v1

Gen.Rel.Grav. 38 (2006) 735-742

Physics

Quantum Physics

9 pages, one eps figure

Scientific paper

10.1007/s10714-006-0262-9

String theory, quantum geometry, loop quantum gravity and black hole physics all indicate the existence of a minimal observable length on the order of Planck length. This feature leads to a modification of Heisenberg uncertainty principle. Such a modified Heisenberg uncertainty principle is referred as gravitational uncertainty principle(GUP) in literatures. This proposal has some novel implications on various domains of theoretical physics. Here, we study some consequences of GUP in the spirit of Quantum mechanics. We consider two problem: a particle in an one-dimensional box and momentum space wave function for a "free particle". In each case we will solve corresponding perturbational equations and compare the results with ordinary solutions.

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