Dynamical noncommutative quantum mechanics

We study some basic and interesting quantum mechanical systems in dynamical noncommutative spaces in which the space-space commutation relations are position dependent. It is observed that the fundamental objects in the dynamical noncommutative space introduced here are string-like. We show that the Stark effect can be employed to determine whether the noncommutativity of space is dynamical or non-dynamical. It appears that unlike a non-dynamical case there is a fundamental energy tau h(2)/m in this dynamical space.