We investigate properties of generalized time-dependent $q$-deformed coherent states for a noncommutative harmonic oscillator. The states are shown to satisfy a generalized version of Heisenberg’s uncertainty relations. For the initial value in time the states are demonstrated to be squeezed, i.e., the inequalities are saturated, whereas when time evolves the uncertainty product oscillates away from this value albeit still respecting the relations. For the canonical variables on a noncommutative space we verify explicitly that Ehrenfest’s theorem holds at all times. We conjecture that the model exhibits revival times to infinite order. Explicit sample computations for the fractional revival times and superrevival times are presented.

• Received 7 December 2012

DOI:https://doi.org/10.1103/PhysRevD.87.084033