Uncertainty Relations and Wave Packets on the Quantum Plane

(2+2)–dimensional quantum mechanical q–phase space which is the semi– direct product of the quantum planeEq(2)/U(1) and its dual algebra eq(2)/u(1) is constructed. Commutation and the resulting uncertainty relations are studied. ”Quantum mechanical q–Hamiltonian” of the motion over the quantum plane is derived and the solution of the Schrödinger equation for the q– semiclassical motion governed by the expectation value of that Hamiltonian is solved.