a Study of Decay in Quantum Mechanics.

Mark S. Hillery

Vladimir I. Kruglov, Konstantin A. Makarov, B. S. Pavlov +1 more

K.J.F. Gaemers, T.D. Visser

D. S. Onley, Anita Kumar

A simple quantum-mechanical model consisting of a two-level system coupled to a continuum, where the interaction can be varied from perturbative to strong, is examined for what can be learned about quantum mechanical decay using elementary methods. The decay spectrum and time dependence of the amplitudes can be calculated in this model, without resorting to perturbation theory. The spectrum is not precisely Lorentzian nor is the decay precisely exponential, features that appear to be shared by all quantum-mechanical models of decaying systems. The conditions for exponential decay and some of the reasons for deviation from this at both short and long times are discussed.

George Jaroszkiewicz

Using the formalism of system-free quantum mechanics, we show how quantum mechanical particle decay probabilities can be discussed rigorously within a framework that conserves total probability, requiring neither non-Hermitian Hamiltonians nor the ad-hoc introduction of complex energies. We apply our formalism to single channel decays, the ammonium molecule, and neutral Kaon decay processes.

Francesco Giacosa

We describe some salient features as well as some recent developments concerning short-time deviations from the exponential decay law in the context of Quantum Mechanics by using the Lee Hamiltonian approach and Quantum Field Theory by using relativistic Lagrangians. In particular, the case in which two decay channels are present is analyzed: the ratio of decay probability densities, which is a constant equal to the ratio of decay widths in the exponential limit, shows in general sizable fluctuations which persist also at long times.