Time evolution of quantum resonance states

Abstract

Let H₀ be self-adjoint with E₀ a possibly degenerate eigenvalue embedded in the continuous spectrum σ_c(H₀) and ψ₀ a normalized eigenfunction. For a certain class of perturbations W and H=H₀+W we investigate the asymptotics of the (naive) resonance state e^−itHψ₀ in the limit W→0. This amplifies previous results of Merkli and Sigal.