Remarks to the resonance-decay problem in quantum mechanics from a mathematical point of view
From MaRDI portal
Publication:2330899
DOI10.1007/978-3-030-01156-7_34zbMATH Open1423.81186arXiv1706.04137OpenAlexW2626633871MaRDI QIDQ2330899
Publication date: 23 October 2019
Abstract: The description of bumps in scattering cross-sections by Breit-Wigner amplitudes led in the framework of the mathematical Physics to its formulation as the so-called Resonance-Decay Problem. It consists of a spectraltheoretical component and the connection of this component with the construction of decaying states. First the note quotes a solution for scattering systems, where the absolutely continuous parts of the Hamiltonians are semi-bounded and the scattering matrix is holomorphic in the upper half plane. This result uses the approach developed by Lax and Phillips, where the energy scale is extended to the whole real axis. The relationship of the spectraltheoretical part of its solution and corresponding solutions obtained by other approaches is explained in the case of the Friedrichs model. A No-Go theorem shows the impossibility of the total solution within the specific framework of non-relativistic quantum mechanics. This points to the importance of the Lax-Phillips approach. At last, a solution is presented, where the scattering matrix is meromorphic in the upper half plane.
Full work available at URL: https://arxiv.org/abs/1706.04137
This page was built for publication: Remarks to the resonance-decay problem in quantum mechanics from a mathematical point of view
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q2330899)
