On the generalized Friedrichs-Lee model with multiple discrete and continuous states*

Abstract In this study, we present several improvements of the non-relativistic Friedrichs-Lee model with multiple discrete and continuous states while retaining its solvability. Our findings establish a solid theoretical basis for the exploration of resonance phenomena in scenarios involving multiple interfering states across various channels. The scattering amplitudes associated with the continuum states naturally adhere to coupled-channel unitarity, rendering this framework particularly valuable for investigating hadronic resonant states appearing in multiple coupled channels. Moreover, this generalized framework exhibits a wide-range applicability, enabling investigations into resonance phenomena across diverse physical domains, including hadron physics, nuclear physics, optics, cold atom physics, etc.