  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.
