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Time Evolution of Quantum Resonance States

Klein, Markus; Rama, Juliane; Wüst, Rainer

Inst. Mathematik

Let $H_0$ be self-adjoint with $E_0$ a possibly degenerate eigenvalue in the continuous spectrum $\sigma_c(H_0)$ and and $\psi_0$ a normalized eigenfunction. For a certain class of perturbations $W$ and $H=H_0+W$ we investigate the asymptotics of the (naive) resonance state $e^{-itH}\psi_0$ in the limit $W \to 0$. This amplifies previous results of Merkli and Sigal.