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

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