Unstable States in a Model of Nonrelativistic Quantum Electrodynamics: Corrections to the Lorentzian Distribution

We revisit the Lee-Friedrichs model as a of atomic resonances in hydrogen atom, using dipole-moment matrix-element functions which have been exactly computed by Nussenzveig. The Hamiltonian H is positive and has absolutely continuous spectrum. Although return probability amplitude $$R_{\Psi }(t) = (\Psi , \exp (-iHt) \Psi )$$ initial state $$\Psi $$ taken so-called Weisskopf–Wigner (W.W.) state, cannot be exactly, we show that it equals sum an exponentially decaying term universal correction $$O(\beta ^{2}\frac{1}{t})$$ for large times t small coupling constants $$\beta improving on some results King (Lett Math Phys 23:215–222, 1991). remaining, non-universal, part also shown to same qualitative type. method consists approximating matrix element resolvent operator W.W. Lorentzian distribution. No use made complex energies associated analytic continuations ”physical” Riemann sheets. Other new are presented, particular physical interpretation corrections, characterization sojourn time $$\tau _{H}(\Psi )= \int _{0}^{\infty } |R_{\Psi }(t)|^{2} dt$$ average lifetime standard quantity (quantum) probability.