by Sagun Chanillo §1. Introduction: Let G denote a Lie group. We are concerned here with the initial value problem for the time dependent Schrödinger eqn., −iu t = ∆u, u| t=0 = f (x), x ∈ G (1.1) ∆ will denote the Laplace-Beltrami operator with respect to an appropriate G invariant metric. Our main aim is to obtain conditions on f which will guarantee that the solution u(x, t), vanishes identic...