THE TIME EVOLUTION OF A CLASS OF META-STABLE STATES

The non-relativistic quantum mechanical description of meta-stable states which arise by perturbation of embedded eigenvalues is considered. The model given by the Hamiltonian [GRAPHICS] is studied for small lambda. If -Delta + v has a positive eigenvalue then, when lambda = 0, H has an embedded eigenvalue. The corresponding eigenstate, Phi, is a meta-stable state for lambda not equal 0. The time evolution of Phi under H,e(-itH)Phi, is estimated uniformly in t.