Bound State Internal Interactions as a Mechanism for Exponential Decay

Abstract: We hypothesize that the uncontrolled interactions among the various components of quantum mechanical bound states and the background fields, sometimes known as virtual particle exchange, affect the state of the quantum system as do typical scattering interactions. Then with the assumption that the interior environment of unstable particles is disordered, we derive in the limit of continuous internal interactions an exactly exponential decay probability at all times and Fermi's Golden Rule for the decay rates. Our result offers a resolution to the long-standing problems with the standard theoretical treatments, such as the lack of exponential time evolution for Hilbert Space vectors and energy spectra unbounded from below.