2019/10/21 by Walter F. Wreszinski, Wreszinski, Walter F.
Physics and Astronomy · #Atomic and Molecular Physics #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1910.09332
openalex publication_date 2019/10/21 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
We review the Lee-Friedrichs model as a model of atomic resonances in the\nhydrogen atom, using the dipole-moment matrix-element functions which have been\nexactly computed by Nussenzveig. The Hamiltonian H of the model is positive\nand has absolutely continuous spectrum. Although the return probability\namplitude R\Ψ(t)=(\Ψ,t\exp(-iHt)\Ψ) of the initial state \Ψ,\ntaken as the so-called Weisskopf-Wigner (W.W.) state, cannot be computed\nexactly, we show that it equals the sum of an exponentially decaying term and a\nuniversal correction O(\β2\(1)/(t)) for large positive times t and\nsmall coupling constants \β, improving on some results of C. King. The\nremaining, non-universal part of the correction is also shown to be of the same\nqualitative type. The method consists in approximating the matrix element of\nthe resolvent operator in the W.W. state by a Lorentzian distribution. No use\nis made of complex energies associated to analytic continuations of the\nresolvent operator to "unphysical" Riemann sheets. Other new results are\npresented, in particular a physical interpretation of the corrections and the\ncharacterization of the so-called sojourn time as the average lifetime of the\ndecaying state, a standard quantity in (quantum) probability.\n