Preprint 17-2005

Time Evolution of Quantum Resonance States

Author(s) : Markus Klein, Juliane Rama, Rainer Wüst

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 17-2005

MSC 2000

47A40 Scattering theory

81U99 None of the above, but in this section

Abstract :
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.

Keywords : resonance state, embedded eigenvalue