Amir Etemadi | Searcharxiv

arXiv2014

A note on Hilbert Space Representation of Quantum Mechanics with Minimal Length

We study some fundamental issues related to the Hilbert space representation of quantum mechanics in the presence of a minimal length and maximal momentum. In this framework, the maximally localized states and quasi-position representation introduced by Kempf et al. are reconsidered and modified. We show that all studies in recent years, including [15] and [16] need serious modification in order to be a consistent framework for quantum mechanics in Planck scale.

gr-qc↗

arXiv2012

Minimal length, maximal momentum and Hilbert space representation of quantum mechanics

Kempf et al. in Ref. [1] have formulated a Hilbert space representation of quantum mechanics with a minimal measurable length. Recently it has been revealed, in the context of doubly special relativity, that a test particles' momentum cannot be arbitrarily imprecise and therefore there is an upper bound for momentum fluctuations. Taking this achievement into account, we generalize the seminal work of Kempf {\it et al.} to the case that there is also a maximal particles' momentum. Existence of an upper bound for the test particles' momentum provides several novel and interesting features, some of which are studied in this paper.

hep-th↗