Localized states in deformed quantum mechanics

Abstract

This Letter describes some elementary properties of coherent states in deformed quantum mechanics. The results are: these states are defined as eigenstates of the annihilation operator of q-algebras; with a specific realization for this operator the coherent states are associated with elements in a Hilbert space of analytic functions, they are minimum uncertainty states after a simple condition is satisfied - necessary for an appropriate definition of the position and momentum operators in terms of the creation and annihilation operators of the q-algebra; a shifting operator is exhibited and finally in this deformed quantum mechanics it is shown that it is possible to have states with negligible uncertainty without having to take the limit to a classical theory.